Question

A projectile is shot upward from a tower 50 meters high. The formula: h = -10t + 40t + 50 gives the height of the projectile above the ground after “t” seconds ( it is on the ground when h = 0 ). Remember the graph of this function is a parabola. Which statement is true? 2

The highest it gets above the ground is 90 meters and it hits the ground after 2 seconds.

The highest it gets above the ground is 80 meters and it hits the ground after 2 seconds.

The highest it gets above the ground is 90 meters and it hits the ground after 5 seconds.

Answer 1

Given that,

A projectile is shot upward from a tower 50 meters high. The height as a function of time is given by :

$h(t)=-10t^2 + 40t + 50$

t is in seconds

Solution,

When it hits the ground, h(t) = 0. So,

$-10t^2 + 40t + 50=0$ .......(1)

On solving the above quadratic equation, we get the value of t as :

t = 5 seconds

It will hit the ground after 5 seconds.

For highest height, differentiate equation (1) wrt t and then put $\dfrac{dh}{dt}=0$, we get :

$\dfrac{dh}{dt}=\dfrac{d}{dt}(-10t^2+40t+50)\\\\\dfrac{dh}{dt}=-20t+40$

$-20t+40=0\\\\t=2\ s$

Put t = 2 in equation (1) :

$h=-10\left(2\right)^{2}+40\left(2\right)+50=90\ m$

Hence, the correct option is (D) "The highest it gets above the ground is 90 meters and it hits the ground after 5 seconds"

Learn more,

projectile motion