Question

In: Math

A rocket is fired upward from some initial height above the ground

11. A rocket is fired upward from some initial height above the ground. Its height h in feet above the ground t seconds after it is fired is given by h = -16t2 + 48t +448.
(i) What is its initial height? __________ ft.
(ii) What is its maximum height? ___________ ft.
(iii) How long does it take to reach the ground? __________ sec.

Solutions

Expert Solution

initial height is when t=0. 448

h = -16(t² - 3t - 28)
= -16(t-7)(t+4)

Note that h=0 when t=7. That's the answer to part iii

Since the two roots are -4 & 7, the apex is reached at t = (-4 + 7)/2 = 1.5

h(1.5) = -16(5.5)(5.5) = 484 ft

milcah answered 2 years ago
Next > < Previous

Related Solutions

A projectile is fired at a height of 2 meters above the ground with an initial...
A projectile is fired at a height of 2 meters above the ground with an initial velocity of 100 meteres per second at an angle of 35° with the horizontal. Round each result to the nearest tenths of a unit. a) Find the vector-valued function describing the motion b) Find the max height c) How long was the projectile in the air d) Find the range
Projectile Motion - From Ground - General Launch Angle A rocket is fired at an initial...
Projectile Motion - From Ground - General Launch Angle A rocket is fired at an initial speed v0 = 160.0 m/s from ground level, at an angle θ = 46° above the horizontal. Ignore air resistance. The magnitude of the gravitational acceleration is 9.8 m/s2. Choose the RIGHT as positive x-direction. Choose UPWARD as psotitive y-direction Keep 2 decimal places in all answers A. Find v0x, the x component of the initial velocity (in m/s) B.Find v0y, the y component...
A ball is tossed vertically upward from a window, height 50.0 m above the ground. The...
A ball is tossed vertically upward from a window, height 50.0 m above the ground. The initial speed of the ball is 25.0 m/s. The ball goes up and comes down, landing on the ground at the base of the building. Determine the following: a) The time it took the ball to reach its maximum height above ground. b) The maximum height above the ground. c) The time the ball returns to its initial height. d) The velocity of the...
The distance s(in m) above the ground for a projectile fired vertically upward with a velocity...
The distance s(in m) above the ground for a projectile fired vertically upward with a velocity of 4(a) m/s as a function of time t(in s) is given by s=4(a)t-4.(b)t2 a= 6 b=9 Find the answers to these questions 1. find t for v=0 2. find v for t=4 3. find v for t=5 what conclusions can you draw?
A model rocket is fired from the ground in a parabolic arc. At the very top...
A model rocket is fired from the ground in a parabolic arc. At the very top of the arc, at a horizontal displacement of 260 m from the launch point, an explosion occurs within the rocket, breaking it into two fragments which separate from each other. One fragment, having 1/3 the mass of the rocket, falls straight down to Earth as if it were at rest at that moment right after the explosion.  Determine the total horizontal displacement from the launch...
A catapult launches a test rocket vertically upward from a well, giving the rocket an initial...
A catapult launches a test rocket vertically upward from a well, giving the rocket an initial speed of 79.4 m/s at ground level. The engines then fire, and the rocket accelerates upward at 3.90 m/s2 until it reaches an altitude of 1200 m. At that point its engines fail, and the rocket goes into free fall, with an acceleration of −9.80 m/s2. (You will need to consider the motion while the engine is operating and the free-fall motion separately.) (a)...
A catapult launches a test rocket vertically upward from a well, giving the rocket an initial...
A catapult launches a test rocket vertically upward from a well, giving the rocket an initial speed of 79.2 m/s at ground level. The engines then fire, and the rocket accelerates upward at 3.90 m/s2 until it reaches an altitude of 1060 m. At that point its engines fail, and the rocket goes into free fall, with an acceleration of −9.80 m/s2. (You will need to consider the motion while the engine is operating and the free-fall motion separately.) (a)...
A catapult launches a test rocket vertically upward from a well, giving the rocket an initial...
A catapult launches a test rocket vertically upward from a well, giving the rocket an initial speed of 80.8 m/s at ground level. The engines then fire, and the rocket accelerates upward at 4.20 m/s2 until it reaches an altitude of 990 m. At that point its engines fail, and the rocket goes into free fall, with an acceleration of ❝9.80 m/s2. (You will need to consider the motion while the engine is operating and the free-fall motion separately.) (a)...
A catapult launches a test rocket vertically upward from a well, giving the rocket an initial...
A catapult launches a test rocket vertically upward from a well, giving the rocket an initial speed of 80.8 m/s at ground level. The engines then fire, and the rocket accelerates upward at 4.20 m/s2 until it reaches an altitude of 990 m. At that point its engines fail, and the rocket goes into free fall, with an acceleration of −9.80 m/s2. (You will need to consider the motion while the engine is operating and the free-fall motion separately.) (a)...
A rocket is fired straight upward, starting from rest with an acceleration of 25.0 m/s2. It...
A rocket is fired straight upward, starting from rest with an acceleration of 25.0 m/s2. It runs out of fuel at the end of 4.00 s and continues to coast upward, reaching a maximum height before falling back to Earth. (a) Find the rocket’s height when it runs out of fuel; (b) find the rocket’s velocity when it runs out of fuel; (c) find the maximum height the rocket reaches; (d) find the rocket’s velocity the instant before the rocket...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT