1. A rock is thrown upward from a level ground in such a way that the maximum he

Question

1. A rock is thrown upward from a level ground in such a way that the maximum
height of its flight is equal to its horizontal range. At what angle is the rock
thrown?

2. A projectile is fired with a velocity of 602 m/s northeast.
a. How long does it take for the ball to reach its highest point?
b. What horizontal distance does the ball travel in this time?

3. A bullet is fired horizontally with a velocity of 900 m/s at a target located 150 m from the rifle. how far does the bullet fall when it reaches the target?

4. A rocket with a constant velocity of 802 m/s in the direction northeast hits a projectile after 3 s. If the projectile was launched from the ground 10s before the collision, what is the initial vertical speed of the projectile and maximum height?

Explanation / Answer

1)We know that the maximum height is given by:

H = v^2/2g

where, v = vy = v sin(theta)

H = v^2 sin^2(theta)/2g

range of the projectile is:

R = vx T = v cos(theta) t

t = H/vy = v^2 sin^2(theta)/2g x v sin(theta)

t = v sin(theta)/2g

R = v^2 cos(theta) sin(theta)/2g

R = H

v^2 cos(theta) sin(theta)/2g = v^2 sin^(theta)/2g

cos(theta) = sin(theta)

sin(theta)/cos(theta) = 1

tan(theta) = 1

theta = tan^-1(1) = 45 deg

Hence, theta = 45 deg

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