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Questions tagged [projectile-motion]

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1answer
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Projectile Motion: Finding an angle that will land at certain coordinates [on hold]

I have been trying to work this out for a ridiculously long time. I need to land at coordinates 10,140 from my "Base" which is 177,200. I have been counting my initial y coordinate as 0, however, as ...
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0answers
8 views

M3 proving SHM for particle on 2 strings

Two light strings of natural length a and modulus of elasticity 6mg are attached at their ends to a particle P of mass m. The other ends of the strings are attached to two fixed points A and B, which ...
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13 views

SUVAT Projectiles - Range R and Max height H

Any help with the highlighted task below? Of course there's multiple ways to express the velocity and angle, however I am struggling to find the required. Thanks Projectiles
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1answer
18 views

Parabolic shot problem

In a parabolic shot thrown at an angle $\Theta$ with respect to the horizontal, it is known that the radius of curvature at the point where the object is thrown (labeled as point $A$) is $p_A$. ...
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2answers
19 views

Complex SUVAT help?

Two objects are dropped from the top of a cliff height $H.$ The second is dropped when the first has travelled a distance $D.$ Prove that the instant when the first object has reached bottom, the ...
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0answers
31 views

How to solve Linear motion problem

At point K a particle which is at rest starts motion when $t=0$ it moves with a uniform acceleration $f_1$ for a period of $t_1$. Then it decelerates by $f_2$ for a period of $t_2$. Then it ...
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1answer
24 views

A Projectile Motion Problem

I need more help, but this time it if for a problem involving projectile motion. The question is " A shot leaves the thrower’s hand 6.5 ft above the ground at a 45° angle at 44 ft / sec. Where is it ...
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1answer
30 views

Physics with Kinematics and Projectile motion

A $0.1$ kg nut is thrown by a squirrel off of the top of a $10$ m tall tree. It is thrown with an initial upward velocity of $4$ m/s and an initial horizontal velocity of $3$ m/s. a) How long till ...
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2answers
41 views

Projectile motion, initial angle and velocity

Question: A projectile motion passes $(16i+7.1j)$, $(0i+0j)$ and $(32i+4.4j)$. Determine the initial speed and velocity. (At the origin) My attempt: I converted the $i$ and $j$ in $x$ and $y$ to ...
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2answers
63 views

Projectile Motion, finding the optimal angle

I've been studying multivariable calculus the last 2 weeks, and I understand (I think) how to optimize 2 variable equations through normal optimization and constrained optimization via Lagrange. I ...
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1answer
46 views

Air resistance in projectile motion

Good morning mathematicians, I would like to ask you for good resources for modelling projectile motion under air resistance. I have not been able to find any good sources. Thank you in advance.
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1answer
48 views

Projectile Motion with Wind Effect

My first question is about the former question Projectile Motion with Air Resistance and Wind 1, could you suggest a book or article and an example given about wind effect. My second question is ...
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1answer
17 views

Calculating all components of Projectile motion

I have a Physics project which requires me to find football passes and calculate based on the data given. I need to find the Initial Velocity, Angle of Release, and max height with only the time and ...
3
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1answer
42 views

Finding Projectile Angle With Different Elevation When Velocity And Range Are Known

I'm trying to derive a formula to find the angle $θ$ required to hit a target that may be higher or lower than the initial launch position. My known variables are $g, v_0, y_0, y_f, x_0, x_f$ where: ...
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1answer
37 views

Time of flight of projectile from launch to landing

The formula below is the time of flight ( time of whole journey from launch(0,0) to landing (×,y) ) of a projectile whose initial vertical position is above the point of impact. I am trying to ...
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1answer
36 views

How to graph the motion of a projectile?

Suppose I have a projectile, fired at angle $\theta$, with velocity $v_0$, assuming it's only acted upon by gravity. How can I find an equation to enable me to plot the motion (vertical height against ...
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1answer
53 views

Projectile Motion - Speed Variations has no impact

https://www.youtube.com/watch?v=0jGZnMf3rPo Explain why the bullet would always hit the monkey by solving the projectile problem. Despite the initial speed to be of 13m/s or 9m/s, the monkey gets ...
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0answers
36 views

Projectile Envelope - Alternative Derivation?

(see Desmos implementation here) Consider a projectile $P$ launched from the origin at launch velocity $v$ and launch angle $\alpha$. It can be shown easily that the envelope of projectile ...
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1answer
42 views

Finding the range of launch speeds for which water shot from a hose will enter a tank a distance away

A water hose is used to fill a large cylindrical storage tank of diameter $D$ and height $2D$. The hose shoots the water at $45^\circ$ above the horizontal from the same level as the base of the tank ...
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2answers
40 views

How to know 2 unknown variables using 2 equations?

Trying to make my AI hit people. So I need a formula to know the time until my projectile will hit the target and also the direction the projectile should be shot at. Here is an example scenario. ...
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1answer
94 views

Projectile Envelope

Consider a projectile launched from the origin at velocity $v$ and angle $\theta$. From this other question we see several approaches to arrive at the equation for the envelope of different ...
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1answer
29 views

projectile trajectory vector calculus

I have done the part a) and have some understanding of what is going on in part b), but stack in further actions At time t a particle has a velocity v(t) = [2cos(t)]i [4sin(t)cos(t)]j, t 0 and at ...
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2answers
153 views

Projectile Motion using Calculus

A ball is thrown from a height of 6 ft at an angle of 60 degrees with the horizontal. If the ball lands $200$ ft away, what was the initial speed? I know of the equation $$x_{\text{range}}= \frac{...
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0answers
22 views

Discrepancy in computing time in air (2D projectile motion)

A cannonball is fired from a cannon with a velocity of $24.0\,\frac{\mathrm m}{\mathrm s}$ at an angle of $40^\circ$ relative to the positive $x$-axis. It lands on the ground $56.6\,\mathrm m$ from ...
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2answers
101 views

Transformation from Circle to Parabola

$\hspace{2cm}$ Is there a transform that maps points on the circle $$x^2+(y-R)^2=R^2$$ to points on the parabola $$\frac {x^2}{d^2}+\frac y{\frac {d^2}{2(d-R)}}=1$$ as shown by black arrows in the ...
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1answer
90 views

Parabola touching a circle

The parabola $\dfrac {x^2}{d^2}+\dfrac yh=1$ touches the circle $x^2+(y-R)^2=R^2$ at two points, $(\pm p, q)$. It can be easily shown geometrically that $p=\sqrt{2qR-q^2}$. Can it be shown ...
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4answers
53 views

Using derivatives to compute velocity if only displacement is given

I am reading about the Chain Rule of derivative and encountered this problem: If a ball is flying at an angle of π/4, what is the required velocity so it will reach 40 foot high and 350 feet ...
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0answers
21 views

The locus of a point moving toward an another moving point

Let A be a point at the origin of a plane and B(0;50). A moves along the Ox axis while B moves toward A. The rate which A moves is 0.5 unit per second while the rate which B moves is 3 units per ...
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0answers
44 views

Projectile Motion Clarification: Ball Passing Through Inclined Hole

I want to write a projectile motion question where a spherical ball is launched from the ground with, say, initial velocity $ v $ (applied to the center of the ball) and angle of projection $ \theta $,...
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4answers
1k views

Correct formula to find the range of a projectile (given angle (possibly negative), initial velocity, initial elevation, and g)

Given: $\theta$ (a negative angle) $v_0$ (initial velocity) $y_0$ (initial height) $g$ (acceleration of gravity) I want to find the range of a projectile (ignoring wind resistance) Hours of ...
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2answers
287 views

how to find the horizontal position where a projectile lands with inital height, initial velocity and angle

I am trying to find the horizontal position where a projectile lands. I have been given the initial height, initial velocity and the angle in degrees the projectile is launched at. I have tried ...
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1answer
19 views

Projectile - Defined by any two variables, except $h$ and $t$?

Consider the following variables for a projectile: launch velocity $v$ launch angle $\theta$ horizontal range $r$ maximum height $h$ total time taken $t$ It can be easily shown that the projectile ...
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1answer
89 views

Calculus - Find the position and velocity of an object when it hits the ground - using vector

If an object is thrown in the air with an initial position of $(0,0,4)$ in feet and initial velocity $(200,0,256)$ in feet per second, and the acceleration is $(0,8,-32)$. Find the position and ...
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0answers
67 views

Issues with predicting a projectile motion by Euler's method

I am trying to predict the projectile motion of a basketball. Please not that I am not considering any effect of air drag, just the effect of g.I am using euler's method for this purpose. I am able ...
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1answer
42 views

Trajectory of kicked ball

A ball is kicked from the ground with a vertical velocity of $10 m/s$; how long does it take the ball to reach maximum height above ground? I used equation $v=u+at$ but rearranged it and used the $9....
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2answers
141 views

What is minimum speed needed to throw object over a wall that height h and at distance d?

(I am not expert in English. I will write as well as I can.) I ask this question because I want to solve (What is minimum speed needed to jump over sphere object that has radius R and at distance d?)...
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2answers
564 views

Projectile motion with air resistance proportional to velocity squared, system of DE's.

A plane flies at a constant altitude of 1000 ft with a constant speed of 300 mph. The plane drops a relief package to a person on the ground. Assume the origin is point where the supply pack is ...
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5answers
364 views

What is minimum speed needed to jump over sphere object that has radius R and at distance d?

(I am not expert in English. I will write as well as I can.) To understand this question easier, lets see this picture. From this picture, what is minimum initial speed that this grasshopper need to ...
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1answer
28 views

Equation of motion in 2D

Whilst researching for a motion related software issue, I came across the following on Wikipedia "using 2D vectors, the equation $v^2 = u^2 + 2as$ becomes $v^2 = u^2 + 2a \bullet (r - r_0)$" (...
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1answer
39 views

Help with a mechanics question on forces and motion [closed]

I’m having some trouble with a worksheet I was given for undergraduate mechanics. I didn’t have any lectures in this topic due to strikes happening at my university, so any help with how to answer ...
0
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1answer
61 views

Projectile initial speed with maximum range and height.

A projectile has range R and maximum height H. Prove that the initial speed is $\sqrt{\frac{g(R^2+16H^2)}{8H}}$ I got the following equations: Vertically: $H=utsin \theta -gt^2/2$,$usin \theta =gt$, $...
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1answer
42 views

Using ODEs in projectile motion

If a cannon fires a cannon ball, where the only other forces are gravity and friction (denoted $pv$, where $v$ is velocity and $p$ is a constant), what would the horizontal equation be in terms of ...
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1answer
298 views

Calculating initial velocity and angle given displacement

The scenario: A diver leaves a $3m$ board on a trajectory that takes her $2.3 m$ above the board and then into the water 2.9 m horizontally from the end of the board. The questions: a) At what ...
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2answers
131 views

Determine the velocity of the skater when they reach the point at the bottom of the halfpipe

A skateboarder with a mass of $75$ kg rolls down a parabolic halfpipe (with shape described by the function $y = 0.2 x^2$). When the skateboarder is at a point $h_1 = 3$m above the ground, their ...
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1answer
327 views

finding initial vertical velocity and final vertical velocity - projectile motion [closed]

find initial vertical velocity and final vertical velocity when a ball has a mass of 280g, flight time of 0.69s and has a length of 0.76m. height of strike is 0.8m. this is a projectile motion ...
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4answers
576 views

Projectile: $v^*w^*=gk$ for minimum launch velocity

A projectile launched from $O(0,0)$ at velocity $v$ and launch angle $\theta$, passes through $P(k,h)$. The velocity of the projectile at $P$ is $w$. The slope of $OP$ is $\alpha$, i.e. $\tan\alpha=\...
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1answer
1k views

Show the maximum height of particle

I have the question "A particle is projected so that the horizontal and vertical components of its initial velocity are U and V respectively. Show that the maximum height of the particle is: V^2 / ...
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1answer
144 views

Arrow fired from height h metres projectiles

I have the question "An arrow is fired from a height h meters at a speed of 55 m/s and at an angle of 5 degrees above the horizontal. The arrow hits a target at a horizontal distance of 60 m from ...
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0answers
281 views

Projectile motion question involving a bullet

I have the question A bullet is fired horizontally at a speed of $65$ m/s from the top of a vertical cliff overlooking the sea. The height of the cliff is $10$ m. Calculate: a) The ...
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1answer
253 views

Particle projected at angle α from foot of plane inclined to horizontal at angle β. Show that it will strike plane at right angles if cotβ=2∗tan(α−β)

A particle is projected at an angle $\alpha$ with the horizontal from foot of the plane, whose inclination to horizontal is $\beta$. Show that it will strike plane at right angles if $ cot \beta = 2*...