The engines of a 1.20 x 10^5 N rocket exert an upward thrust of 2.00 x 10^5 N for 1.50 minutes upon lift off.
What is the impulse exerted on the rocket?
What is the velocity of the rocket at the end of the 1.50 minute period?
To find the impulse exerted on the rocket, we can use the equation:
Impulse = Force * Time
In this case, the force exerted by the engines is 2.00 x 10^5 N, and the time is 1.50 minutes. However, we need to convert the time to seconds to maintain consistency in units. Since there are 60 seconds in a minute, we can multiply 1.50 minutes by 60 to get the time in seconds:
Time = 1.50 minutes * 60 seconds/minute
Time = 90 seconds
Now we can substitute the values into the equation:
Impulse = (2.00 x 10^5 N) * (90 s)
Impulse = 1.80 x 10^7 Ns
So, the impulse exerted on the rocket is 1.80 x 10^7 Ns.
To find the velocity of the rocket at the end of the 1.50 minute period, we can use the equation:
Impulse = Change in Momentum
Since momentum is given by the equation:
Momentum = Mass * Velocity
We can rearrange the equation to solve for velocity:
Velocity = Momentum / Mass
However, we need to find the mass of the rocket to substitute into the equation. We have been given the weight of the rocket, which is 1.20 x 10^5 N.
Weight = Mass * Gravity
To find the mass of the rocket, we need to know the acceleration due to gravity. Assuming it is 9.8 m/s^2, we can rearrange the equation to solve for mass:
Mass = Weight / Gravity
Mass = 1.20 x 10^5 N / 9.8 m/s^2
Mass ≈ 1.22 x 10^4 kg
Now we can substitute the values into the equation:
Velocity = (Impulse) / (Mass)
Velocity = (1.80 x 10^7 Ns) / (1.22 x 10^4 kg)
Velocity ≈ 1.48 x 10^3 m/s
So, the velocity of the rocket at the end of the 1.50 minute period is approximately 1.48 x 10^3 m/s.