Q:

A ball is shot upward from a slingshot at a velocity of 15 m/s the height of the ball after t seconds is given by h(t)=10+ 5t+1/4 t^2 predicted the instantaneous velocity after eight seconds

Accepted Solution

A:
Answer:The instantaneous velocity after eight seconds is 9 m/sStep-by-step explanation:Given as :The ball shot upward with velocity of 15 m/sThe height of the ball after t sec is given as h(t) = [tex]10 + 5t + \frac{1}{4}t^{2}[/tex] Now, The instantaneous velocity after 8 sec = [tex]\frac{\partial h(t)}{\partial t}[/tex]Or, The instantaneous velocity = [tex]\frac{\partial (10 +5t + \frac{1}{4}t^{2})}{\partial t}[/tex] or, The instantaneous velocity = [tex]5 + \frac{1}{4}\times 2 t[/tex]Now at t = 8 secThe instantaneous velocity = 5 + 4 = 9 m/sHence The instantaneous velocity of ball at t = 8 sec , is 9 m/s  Answer