A toy rocket, launched from the ground, rises
vertically with an acceleration of 28 m/s2 for
9.5 s until its motor stops.
Disregarding any air resistance, what max-
imum height above the ground will the rocket
achieve? The acceleration of gravity is
9.8 m/s2 .
Answer in units of km
Vo = a*t = 28 * 9.5 = 266 m/s.
ho = 0.5a*t^2 = 14*9.5^2 = 1264 m.
h = ho + (V^2-Vo^2)/2g
h = 1264 + (0-(266^2)/-19.6 = 4874 m. =
4.874 km.
i tried it but gives me an incorrect answer
To find the maximum height above the ground that the toy rocket will achieve, we need to use the kinematic equation for motion with constant acceleration.
The equation we can use is:
h = V₀t + (1/2)at²
Where:
- h is the height above the ground
- V₀ is the initial velocity, in this case, it is 0 since the rocket starts from rest
- t is the time the rocket is in motion
- a is the acceleration
Since the rocket is rising vertically, we can assume that the motion occurs in the positive direction. Gravity acts in the opposite direction, so we consider it negative.
Given:
- Acceleration of the rocket, a = 28 m/s² (upwards)
- Time the rocket is in motion, t = 9.5 s
- Acceleration due to gravity, g = 9.8 m/s² (downwards)
Now we can substitute these values into the equation and solve for the maximum height, h.
h = 0 * 9.5 + (1/2) * 28 * (9.5)²
Simplifying the equation:
h = 0 + 14 * (9.5)²
h = 14 * (9.5)²
h ≈ 14 * 90.25
h ≈ 1263.5 meters
To convert this to kilometers, divide by 1000:
h ≈ 1263.5 / 1000
h ≈ 1.2635 kilometers
Therefore, the maximum height above the ground that the rocket will achieve is approximately 1.2635 kilometers.