Question

The height of a projectile that is thrown upward from ground level with an initial velocity of 98 meters per second can be modeled by the equation h = −4.9t2 + 98t, where h is the height in meters and t is the elapsed time in seconds. Find the time it takes for the projectile to hit the ground.
10 seconds
20 seconds
15 seconds
5 seconds

Answer 1

It is found that the time it takes for the projectile to hit the ground would be after 20 seconds.

When does the projectile hit the ground?

The projectile would hit the ground when its height h(t), is equal to zero.

The given function that models its height is given by:

$h(t) = -4.9t^2 + 98t.$

where h is the height in meters and t is the elapsed time in seconds.

Then,

h(t) = 0

$-4.9t^2 + 98t = 0\\-4.9t(t - 20) = 0\\\\t - 20 = 0$

t = 20

Thus, The projectile hits the ground after 20 seconds.

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