A 1000kg rocket is moving forward at 10m/s in space. A 10,000N force is applied to the rocket for one second from behind. How fast is the rocket now traveling?
a. 0m/s
b. 10m/s
c. 15m/s
d. 20m/s
F = ma,
a = F / m = 10000 / 1000 = 10m/s^2,
V = Vo + at,
V = 10 + 10*1 = 20m/s.
Resultant force divided by mass
= 10000(force applied) +10000(f=m divided a) =20000 N
20000 N divided by mass 1000kg= 20m/s
To find out the new velocity of the rocket, we need to apply the principle of conservation of momentum. According to this principle, the change in momentum of an object is equal to the force applied to it multiplied by the time interval during which the force is applied.
The initial momentum of the rocket can be calculated using the formula:
Initial momentum = mass * initial velocity
Mass of the rocket = 1000 kg
Initial velocity of the rocket = 10 m/s
Initial momentum = 1000 kg * 10 m/s = 10000 kg·m/s
The force applied to the rocket is 10000 N, and it is applied for 1 second.
Change in momentum = force * time
Change in momentum = 10000 N * 1s = 10000 kg·m/s
According to the principle of conservation of momentum, the change in momentum is equal to the final momentum - initial momentum.
Change in momentum = final momentum - initial momentum
Therefore,
final momentum - initial momentum = 10000 kg·m/s
final momentum = initial momentum + 10000 kg·m/s
final momentum = 10000 kg·m/s + 10000 kg·m/s
final momentum = 20000 kg·m/s
Finally, the final velocity of the rocket can be calculated using the formula:
Final velocity = final momentum / mass
Final velocity = 20000 kg·m/s / 1000 kg
Final velocity = 20 m/s
Therefore, the rocket is now traveling at a speed of 20 m/s.
The correct answer is d. 20m/s.
To solve this problem, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass times its acceleration. We can set up the equation as follows:
Net force = mass x acceleration
In this case, the mass of the rocket is given as 1000kg, and the net force is 10,000N. We need to find the acceleration. We can rearrange the equation to solve for acceleration:
acceleration = Net force / mass
Plugging in the known values:
acceleration = 10,000N / 1000kg
Simplifying the equation, we find:
acceleration = 10m/s^2
Now that we know the acceleration, we can use the equation for constant acceleration to find the change in velocity.
Change in velocity = acceleration x time
In this case, the acceleration is 10m/s^2, and the time is 1 second:
Change in velocity = 10m/s^2 x 1s
The change in velocity is therefore 10m/s.
Since the rocket was already moving forward at 10m/s, the final velocity will be the sum of the initial velocity and the change in velocity:
Final velocity = Initial velocity + Change in velocity
Final velocity = 10m/s + 10m/s
Final velocity = 20m/s
Therefore, the correct answer is d. 20m/s.