# Determine the characteristics of the path of the ball described below.A ball of mass 0.5kg, initially at rest, is kicked directly toward a fence from a point 20m away. The velocity of the ball as...

Determine the characteristics of the path of the ball described below.

A ball of mass 0.5kg, initially at rest, is kicked directly toward a fence from a point 20m away. The velocity of the ball as it leaves the kicker's foot is 17m/s at angle of 47 degrees above the horizontal. The top of the fence is 6m high. The ball hits nothing while in flight and air resistance is negligible. The acceleration due to gravity is 9.8m/s^2.

Determine the time it takes for the ball to reach the plane of the fence. Answer in units of s

How far above the top of fence will the ball pass? Consider the diameter of the ball to be negligible. Answer in units of m

What is the vertical component of the velocity when the ball reaches the plane of the fence? Answer in units of m/s

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### 1 Answer

A ball of mass 0.5kg, initially at rest, is kicked directly toward a fence from a point 20m away. The velocity of the ball as it leaves the kicker's foot is 17m/s at angle of 47 degrees above the horizontal. The top of the fence is 6m high. The ball hits nothing while in flight and air resistance is negligible. The acceleration due to gravity is 9.8m/s^2.

The horizontal component of the velocity with which the ball is kicked is 17*cos 47, this does not change as the ball moves. The vertical component of the velocity of with which the ball is kicked is 17*sin 47. This decreases at the rate of 9.8 m/s^2.

The fence is 20 m away from where it is kicked. The time taken by the ball to reach the plane of the fence is 20/(17*cos 47) = 1.725 s

The height of the ball after 1.725 s is equal to 17*sin 47*1.725 - (1/2)*9.8*(1.725)^2 = 6.86 m.

The vertical component of the velocity of the ball when it reaches the plane of the fence is 17*sin 47 - 9.8*1.725 = -4.47 m/s . The velocity is acting downwards.