Question

A toy rocket is s feet above the Earth at the end of t seconds, where

= −16^(2) + 48√2 ()
a. Find the time it will take to reach the maximum height. Give the exact answer and an approximated answer to two decimal places.
b. Find the maximum height of the rocket. Use the exact answer from part “a” to find this.
c. Find the time it will take for the rocket to strike the ground. Round the answer to two decimal places.

Answer 1

a. The time it will take to reach the maximum height is t= 2
`√(2)` seconds and t≈1.41 seconds (approximated to two decimal places).

b. The maximum height of the rocket is s=48 feet (using the exact answer from part "a").

c. The time it will take for the rocket to strike the ground is t=2
`√(2)` seconds (rounded to two decimal places).

a. To find the time it takes for the rocket to reach its maximum height, we set the velocity equation v(t)=−16t^2 +48
`√(2)` equal to zero since the velocity is zero at the maximum height. Solving for t, we get t=2​ seconds, providing the exact answer. The approximated answer is t≈1.41 seconds, rounded to two decimal places.

b. Using the exact time t= 2​ from part "a," we substitute this into the height equation s(t)=−16t^2 +48
`√(2)` t to find the maximum height. The result is s=48 feet.

c. To determine the time it takes for the rocket to strike the ground, we set the height equation s(t)=−16t^2 +48
`√(2)` t equal to zero since the height is zero when the rocket hits the ground. Solving for t, we get t=2
`√(2)` seconds, rounded to two decimal places.