1.) A ball is thrown off a 50-meter cliff with an initial velocity of 20 meters per second at an angle of 30 degrees above the horizontal. What is the velocity of the horizontal component of the ball's motion?
2.) A force of 100N acts on a 80kg body for 4 seconds. Find the impulse produced by the force and the resulting change in momentum of the body.
Find Impulse and momentum
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Answer:
1.) To find the velocity of the horizontal component of the ball's motion, we need to use trigonometry. The horizontal component of the velocity is given by:
v_horizontal = v_initial * cos(theta)
where v_initial is the initial velocity of the ball and theta is the angle of the initial velocity above the horizontal. Substituting the given values, we get:
v_horizontal = 20 m/s * cos(30 degrees)
v_horizontal = 17.32 m/s
Therefore, the velocity of the horizontal component of the ball's motion is 17.32 m/s.
2.) The impulse produced by the force is given by:
impulse = force * time
Substituting the given values, we get:
impulse = 100 N * 4 s
impulse = 400 Ns
The resulting change in momentum of the body is given by:
change in momentum = impulse
Since the mass of the body is 80 kg, we can calculate the resulting change in velocity using the formula:
change in momentum = mass * change in velocity
Rearranging the formula, we get:
change in velocity = change in momentum / mass
Substituting the value of impulse and mass, we get:
change in velocity = 400 Ns / 80 kg
change in velocity = 5 m/s
Therefore, the resulting change in momentum of the body is 400 Ns and the resulting change in velocity is 5 m/s.