Question

7. Suppose that a golf ball is thrown vertically with an initial velocity of 40 meters per second. Answer the following questions given that the ball’s height (in meters) after t seconds is represented by the function ℎ(t)= −4.9t² + 40t. Use appropriate units for full credit. [15 points]

a. How long will it take for the ball to hit the ground?

b. What will the ball’s instantaneous velocity at t = 5 seconds?

c. Use your answer to (b) to describe the direction in which the ball is traveling at t = 5 seconds.

Answer 1

7A.

Given that position of ball at time 't' is

h(t) = -4.9*t^2 + 40t

Now when ball hits the ground, then at that height of ball will be zero, So

0 = -4.9*t^2 + 40*t

t*(40 - 4.9*t) = 0

t = 40/4.9

t = 8.16 sec = time taken by ball to hit the ground

7B.

we know that velocity at time 't' will be:

V(t) = d(h(t))/dt = d[-4.9*t^2 + 40*t]/dt

V(t) = -4.9*2*t + 40

V(t) = 40 - 9.8*t

Now at t = 5 sec, velocity will be:

V(5) = 40 - 9.8*5

V(5) = -9 m/s

Part C.

-ve sign meaning ball will be traveling in downward direction. Which means ball which was initially going upward, reached at maximum height and after that changed it's direction and now at this time was moving in downward direction.

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