model rocket is launched straight upward with an initial speed of 50.0 m/s. It accelerates with a constant upward acceleration of 1.00 m/s2 until its engines stop at an altitude of 130 m.
(a) What is the maximum height reached by the rocket?
m
(b) How long after lift-off does the rocket reach its maximum height?
s
(c) How long is the rocket in the air?
s
Follow the approach outlined in this similar question of a few days ago:
http://www.jiskha.com/display.cgi?id=1283656710
A certain car is capable of accelerating at a rate of +0.60 m/s2. How long does it take for this car to go from a speed of 20 mi/h to a speed of 65 mi/h?
idk whats the answer
To solve this problem, we can use the kinematic equations of motion. Let's break down each part of the problem:
(a) What is the maximum height reached by the rocket?
To find the maximum height reached by the rocket, we need to determine the time it takes for the rocket to stop accelerating and reach its maximum height. We can use the equation:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s at maximum height)
u = initial velocity (50.0 m/s)
a = acceleration (1.00 m/s^2)
s = displacement (maximum height)
Rearranging the equation, we have:
s = (v^2 - u^2) / (2a)
Substituting the values, we get:
s = (0^2 - 50.0^2) / (2 * (-1.00))
s = -2500 / -2
s = 1250 m
Therefore, the maximum height reached by the rocket is 1250 m.
(b) How long after lift-off does the rocket reach its maximum height?
To figure out the time it takes for the rocket to reach its maximum height, we can use the equation:
v = u + at
Where:
v = final velocity (0 m/s at maximum height)
u = initial velocity (50.0 m/s)
a = acceleration (1.00 m/s^2)
t = time
Rearranging the equation, we get:
t = (v - u) / a
Substituting the values, we have:
t = (0 - 50.0) / (-1.00)
t = 50.0 / 1.00
t = 50.0 s
Therefore, the rocket reaches its maximum height 50.0 seconds after lift-off.
(c) How long is the rocket in the air?
To determine the time the rocket is in the air, we can add twice the time it takes to reach the maximum height to the time it takes to reach the maximum height.
The time it takes to reach the maximum height is 50.0 seconds.
Therefore, the total time the rocket is in the air is:
2 * 50 + 50 = 150.0 seconds
Therefore, the rocket is in the air for 150.0 seconds.