Question

A ball is thrown directly upwards from a height of 7 ft with an initial velocity of 20 ft/sec. The function s(t)= -16t^2 + 20t + 7 gives the height of the ball, in feet, t seconds after it has been thrown. Determine the time at which the bar which is it’s maximum height and find the maximum height.The ball reaches its maximum height of__ ft__ sec(s) after the ball is thrown

Answer 1

We are given the function: s(t)= -16t^2 + 20t + 7

(i) We will determine the time at which the bar which is it’s maximum height as follows : find the vertex .

• Vertex (t ), = -b/2a ; where a = -16 , b = 20

= -20/2(-16)

=-20/-32

=0.625 seconds

• Therefore, the time in which the ball reaches the maximum height is 0.625 Second,s.

(ii) Calculating the maximum height: ( y- value t maximum point {0.625} )

s(t)= -16t^2 + 20t + 7

→s(0.625) = -16(0.625)^2 + 20(0.625) + 7

=-6.25 + 12.5 +7

=13.25ft

• Thererefore, the maximum height reached by the ball is 13.25ft.