Question

If an object is projected vertically upward with a velocity of 29.4 m/s from a height of 30 m, then its height h above the ground in meters after t seconds is given by h = 30 + 29.4t - 4.9t^2. What is the maximum height the object will reach?

If you could show work, that would be excellent. Thank you!

Answer 1

Explanation:

we can determine the maximum height using the expression given after finding the value of time at which the object reaches the maximum height. In order to find the time at which the object reaches the maximum height we need to use one of the UAM formulas.

and the compatible UAM formula is: vf=vi+at, we use UAM formula because the object is uniformly accelerating due to gravitational force.

vf=vi+at, at the point where the object reaches the maximum height its velocity will be zero so vf=0 and vi=29.4m/s.

given

a=-9.8m/s^2

vf=0

vi=29.4m/s

t=?

0=29.4-(9.8)t

-29.4= -9.8t

t= 29.4/9.8

t=3 seconds, it takes 3 seconds to reach the maximum height starting from a height of 30m.

h=30+29.4(3)-4.9(3)^2

h=30+88.2-44.1

h=118.2-44.1

h=74.1 m