Question

Solve:

a) A ball rolls horizontally off a cliff at a speed of 30 m/s. It takes about 7 seconds for the ball to hit the ground. Calculate the height of the cliff and the horizontal distance traveled by the ball.
b) A ball rolls off a building that is 100m high. Calculate the time that it takes for the ball to hit the ground
c) A soccer ball is kicked horizontally from the roof of a building 150m tall and lands about 200m from the base of the building. Calculate the initial speed of the ball.

Answer 1

To solve these problems, we can use the kinematic equations for projectile motion. For part (a), the time of flight can be found using the formula: time = distance / velocity. For part (b), the time of flight can be found using the formula: time = 2 * vertical velocity / gravity. For part (c), we can use the formula for horizontal distance: distance = vertical velocity * time.

Step-by-step explanation:

To solve these problems, we can use the kinematic equations for projectile motion.

For part (a), we know the horizontal distance traveled by the ball is 100.0m and the initial horizontal velocity is the same as the final horizontal velocity since there is no acceleration in the horizontal direction. Therefore, the time of flight can be found using the formula: time = distance / velocity. In this case, time = 100.0m / 30m/s = 3.33s.

For part (b), the time of flight can be found using the formula: time = 2 * vertical velocity / gravity. In this case, the vertical velocity is 0 because the ball starts and ends at the same height. Therefore, the time of flight is 0s.

For part (c), we can use the formula for horizontal distance: distance = vertical velocity * time. In this case, the horizontal distance is 200m and the time of flight is 3.33s, so we can find the vertical velocity using the formula: vertical velocity = distance / time = 200m / 3.33s = 60m/s.