# Projectile Questions: Calculate Velocity and Height of Golf Ball | Help Needed

• mcintyre_ie
In summary: Sx*cos(30)+Sy*sin(30))/2. Therefore, the height of the particle is 10ã3t+4.9t^2= 15+9.2t^2. So the max height of the particle is 15+9.2t^2=26.4t.
mcintyre_ie
Hey
I need a little help with another projectile question, id be very obliged if anybody could provide some:

(A) A golf ball at rest on horizontal ground is struck so that it starts to move with velocity 3u I + u j ( “I” and “j” are unit vectors along and perpendicular to the ground) . In its flight, the ball rises to a max height of 15 m. Calculate:
(i) The value of u
(ii) The magnitude and direction of the velocity with which the ball strikes the ground.

(i) What I've got is Sy = 15m, when Vy = 0, time when Vy = 0 is (u/g).
I then subbed this into Sy= ut - (1/2)gt^2 = 15 and got u =

(ii) Velocity, when Sy=0.
Time when Sy=0 is (2u/g)

I then subbed this into my Vx (3u) and Vy (u - gt) equations to get &radic;2646i - &radic;1176 j.

Im wondering wheter this answer is right, it just doesn't sound right to me, the negative j-value maybe is a bit off?

I then got the Tan of (-&radic;294 / &radic;2646) = -1/3 = -18degrees 26 minutes.
I interpreted this as being E18.26.S, which I am not too sure about and is a partial guess.

Part (B) is where I am really getting stuck:

A particle is projected from a point p with an initial speed 15m/s, down a plane inclined at an angle 30 degrees to the horizontal. The direction of projection is at right angles t the inclined plane. (The plane of projection is vertical and contains the line of greatest slope), Find:
(i) the perpindicular height of the particle above the plane after t seconds and hence, or otherwise, show that the vertical height h of the particle above the plane after t seconds is 10&radic;3t - 4.9t^2.
(ii) The greatest vertical heigt it attains above the plane (the max value of h) correct to two places of decimals.

Ive figured from my sketch that the perpindicular height above the plane is (Sy/cos 30). I am not too sure about how i should go about getting the Ux and Uy though, since the particle is fired at right angles to the plane.
http://community.webshots.com/s/image2/1/11/95/94311195xlEyTI_ph.jpg

from the question i know that Uy is 10-&radic;3, but I am assuming I've got to prove that also. Thats about all I've gotten so far.

I'd appreciate any help, and sorry about the crappy diagram...

Last edited by a moderator:
Any help would be very much appreciated...

It would have helped if you had stated that "Sy" was the height of the ball and Vy the y coordinate of speed instead of just using the variables without definition.

i) What I've got is Sy = 15m, when Vy = 0, time when Vy = 0 is (u/g).
I then subbed this into Sy= ut - (1/2)gt^2 = 15 and got u =
ã294.

Yes, that is correct.

I then subbed this into my Vx (3u) and Vy (u - gt) equations to get ã2646i - ã1176 j.

Im wondering wheter this answer is right, it just doesn't sound right to me, the negative j-value maybe is a bit off?

Your y-value looks to be twice the correct value. Since t= 2u/g,
u- gt= u- g(2u/g)= -u.

When the projectile hits the ground its x-component of velocity is still 3u but its y component is -y (because of the symmetry of the trajectory). Of course, tan(&theta;)= -u/3u= -1/3. I get &theta;= 18 degres 24 minutes approx.

A particle is projected from a point p with an initial speed 15m/s, down a plane inclined at an angle 30 degrees to the horizontal. The direction of projection is at right angles t the inclined plane. (The plane of projection is vertical and contains the line of greatest slope), Find:
(i) the perpindicular height of the particle above the plane after t seconds and hence, or otherwise, show that the vertical height h of the particle above the plane after t seconds is 10ã3t - 4.9t^2.
(ii) The greatest vertical heigt it attains above the plane (the max value of h) correct to two places of decimals.

Yeah, I can see how this would be hard. The way I would do this would be to treat the particle as a regular projectile following a hyperbolic trajectory. Since the inclined plane is 30 degrees down from the horizontal, the initial velocity of the particle is 60 degrees up (so that 60+30=90 is the angle between the plane and the initial speed). The intitial velocity of the particle is given by
Vx= 15 cos(60)= (1/2)15= 7.5 m/s, Vy= 15 sin(60)= 7.5 &radic;(3) m/s.
The position (measured from the initial point) at any t is Sx= 7.5t and Sy= 7.5 &radic;(3) t- 4.9 t2.

Now look at the inclined plane. Since it is inclined 30 degrees downward its slope is tan(-30)= -1/&radic;(3). Its equation is

The height of the particle above the plane is "height of particle - height of plane"= 7.5 &radic;(3)t- 4.9t2+ (1/&radic;(3))(7.5t)

Thanks for the help
Sorry about not defining Sx, Vx, etc, I am just so used to using them all the time i just assumed everybody else was too
Thanks again

## 1. What is a projectile?

A projectile is any object that is thrown or launched into the air and is subject to the force of gravity and air resistance. Examples of projectiles include a baseball, a bullet, or a rocket.

## 2. How does air resistance affect a projectile's motion?

Air resistance, also known as drag, acts opposite to the direction of motion of a projectile and can slow it down. The amount of air resistance depends on the size, shape, and speed of the projectile.

## 3. What factors influence the trajectory of a projectile?

The trajectory, or path, of a projectile is influenced by its initial velocity, angle of launch, air resistance, and the force of gravity. These factors can be manipulated to change the trajectory of a projectile.

## 4. How can projectile motion be calculated?

Projectile motion can be calculated using the equations of motion, which take into account the initial velocity, angle of launch, and acceleration due to gravity. These equations are often used in physics to predict the motion of a projectile.

## 5. What are some real-world applications of projectile motion?

Projectile motion has many practical applications, such as in sports like baseball and golf, where the trajectory of a ball must be carefully calculated. It is also used in engineering for designing structures and machines that involve projectiles, such as catapults and rockets.

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