Question

The benches of a gallery in a cricket stadium are 1 m wide and 1 m high. A batsman strikes the ball at a level one meter above the ground and hits a mammoth sixer. The ball starts at 35 m/s at an angle of 53° with the horizontal. The benches are perpendicular to the plane of motion, and the first bench is 110 m from the batsman. On which bench will the ball hit?

Answer 1

To determine which bench the ball will hit, we can break down the motion of the ball into its horizontal and vertical components. Using the given information, we can find the time it takes for the ball to travel to the first bench. Therefore, the ball will hit the first bench after approximately 2.4 seconds.

Step-by-step explanation:

To determine which bench the ball will hit, we can break down the motion of the ball into its horizontal and vertical components. Since the benches are perpendicular to the plane of motion, we only need to consider the horizontal component.

Using the given information, we can find the time it takes for the ball to travel to the first bench. Using the formula t = d/v, where t is the time, d is the distance, and v is the velocity, we can calculate:

t = 110 m / (35 m/s * cos(53°)) = 2.38037 s

Therefore, the ball will hit the first bench after approximately 2.4 seconds.