Algebra

A toy rocket that is shot in the air with an upward velocity of 48 feet per second can be modeled by the function f(t)=-16t^2+48t , where t is the time in seconds since the rocket was shot and f(t) is the rocket’s height. What is the maximum height the rocket reaches?

16ft
36ft
48ft
or 144 ft

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. Well, that is a parabola. Where is the vertex?

-16 t^2 + 48 t = h

16 t^2 - 48 t = -h

t^2 - 3 t = -(1/16)h

t^2 - 3 t + 9/4 = -(1/16)h + 9/4

(t - 3/2)^2 = -(1/16)(h - 36)

ah ha, hits the vertex at the top when t = 1.5 seconds and h = 36 feet

1. 👍
2. 👎
3. ℹ️
4. 🚩
2. thanks!!

1. 👍
2. 👎
3. ℹ️
4. 🚩
3. You are welcome.

1. 👍
2. 👎
3. ℹ️
4. 🚩

Similar Questions

1. Math

A rocket is launched from the top of a 50 foot cliff with an initial velocity of 120 feet per second. The height, h, of the rocket after t seconds is given by the equation h=-16t^2 + 120t+ 50. How long after the rocket is launched

2. math

A rocket is launch from the top of an 40 foot cliff with an initial velocity of 140 feet per second, the height h of the rocket after t seconds is given by the equation h=16t^2+140t+40. How long after the rocket is launch will be

3. math

A toy rocket is launched straight up into the air with an initial velocity of 60 ft/s from a table 3 ft above the ground. If acceleration due to gravity is –16 ft/s2, approximately how many seconds after the launch will the toy

4. physics

using a powerful air gun, a steel ball is shot vertically upward with a velocity of 80 m/s, followed by another shot after 5 seconds. find the initial velocity of the second ball to meet the first ball 150 m from the ground.

1. Physics

A test rocket is launched vertically from ground level (y=0m), at time t=0.0 s. The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to 97 m and

2. algebra

an arrow is shot into the air with an initial velocity of 96 feet per second. the height in feet of the arrow t seconds after it was shot into the air is given by the function h(x)=-16t^2+96t. find the maximum height of the arrow.

3. Calculus

Camille launches a model rocket in an open field near her house. The rocket has a bit of a problem, being slightly off balance. Its trajectory is described by the function y=60ln(x+1)-6x for 0 ≤ x ≤ 36.15, where y is is the

4. algebra

A toy rocket is launched into the air at an initial velocity of 32 ft/sec, as shown on the graph below. The function s(t)=-16t^2+32t+128 gives the height of the rocket (in feet) at time t (seconds). When does the rocket hit the

1. Physics

A model rocket is launched straight upward with an initial speed of 50 m/s. It accelerates with a constant upward acceleration of 2.00 m/s^2 until its engines stop at an altitude of 150 m. a) What is the max. height reached by the

2. Basic Numeracy and statistics (math)

A rocket is shot into the air with an initial velocity of 800m/sec. The equation h = -16t2+144t models the height of the ball. how long does it take for the rocket to hit the ground (h=0)?

3. Calculus

If a rocket is shot vertically upward from the ground with an initial velocity of 192 ft/sec. a. When does it reach its maximum height above the ground? b. What is the maximum height reached by the rocket? c. How long does it take

4. pre cal

A toy rocket is launched straight up from the roof of a garage with an initial velocity of 56 feet per second. The height h of the rocket in feet, at t seconds after it was launched, is described by h(t)=−16t2+56t+17. Find the