Answer:
a) The maximum height the projectile reaches is 7744 m.
b) The time it takes the object to reach the ground is 44 s.
Step-by-step explanation:
Hi there!
The height function is the following:
h(t) = -16 t² + 704 t
a) Let´s find the time it takes the projectile to reach the maximum height. For this, we can use the fact that at the maximum height, the velocity of the projectile is zero. The velocity is the variation of height with respect to time, in other words, it is the derivative of the height function:
v = dh/dt = -2 · 16 t + 704 = -32 t + 704
At the maximum height:
v = 0
0 = -32 t + 704
-704/-32 = t
t = 22 s
Now, we can calculate the height at time t = 22 s:
h(t) = -16 t² + 704 t
h(22) = -16 (22)² + 704 (22)
h(22) = 7744 m
The maximum height the projectile reaches is 7744 m.
b) When the object reaches the ground h(t) = 0. Then:
h(t) = -16 t² + 704 t
When the object reaches the ground:
0 = -16 t² + 704 t
Let´s solve this quadraic equation for "t":
0 = -16 t² + 704 t
0 = t (-16 t + 704)
t = 0 s
and
-16 t + 704 = 0
-16 t = -704
t = -704/-16
t = 44 s
The time it takes the object to reach the ground is 44 s.