Question

Julie throws a ball to her friend Sarah. The ball leaves Julie's hand a distance 1.5 meters above the ground with an initial speed of 13 m/s at an angle 52 degrees; with respect to the horizontal. Sarah catches the ball 1.5 meters above the ground.

1.What is the maximum height the ball goes above the ground?

2. After catchingt he ball, Sarah throws it back to Julie. The ball leaves Sarah's hand a distance of 1.5 meters above the grounf, and is moving with a speed of 10m/s when it reaches maximum height of 8m above the ground. Wat is the speed of the ball when t leaves Sarah's hand?

3.How high above the ground will the ball be when it gets to Julie?

Answer 1

1. Max height from the point of projection = u²sin²(theta)/2g

H_max = 13^2 * sin²(52)/2*9.8 = 5.35 m

So, max height above the ground = H_max + initial height

= 5.35+1.5 = 6.85 m

Range of projectile = v^2 sin(2*theta)/g = 13^2 * sin(104)/9.8 = 16.73 m

So, distance between sarah and julie = 16.73 m

2. Max height from the point of projection = max height from ground - initial height

Hmax = 8-1.5 = 6.5 m

From the formula of maximum height, we have (u*sin(theta))^2 /2g = 6.5 m,

where u is initial velocity and theta is angle of projection.

u*sin(theta) = 11.28 m/s

At maximum height, vertical component of velocity becomes zero and the ball has only horizontal comp. of velocity.

Horizontal component = u*cos(theta) = 10 m/s

(u*sin(theta))^2 + (u*cos(theta))^2 = u^2 (sin^2 (theta) + cos^2 (theta)) = u^2

since sin^2(theta) + cos^2(theta) = 1 for any angle theta.

substituting in the equation,

11.28^2 + 10^2 = u^2

u = 15.08 m/s

theta = 48.46 degrees

3. From 1, we got that distance between them is 16.73 m

Since horizontal velocity is 10 m/s, time taken for the ball to reach Julie = distance/speed

= 16.73/10 = 1.673 m

Initial vertical velocity = u*sin(theta) = 11.28 m/s

Acceleration in vertical direction = -g = -9.8 m/s^2

So, vertical displacement = ut - 1/2 gt^2

= 11.28*1.673 - 1/2 * 9.8 * 1.673^2

= 5.15 m.

The ball is 5.15 m above the initial height.

So, when Jile catches it, it's height will be 5.15 + 1.5 = 6.65 m