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4 An ice skater and his coach begin stationary and push apart from each other with a force of 75 N. The skater has a mass of 64 kg, whilst the coach weighs 804 N.
If the skater moves off to the left with a speed of 3.6 m s−1, what is the velocity of the coach?
In a stunt for an action movie, the 100 kg actor jumps from a train that is crossing a river bridge.
On the river below, the heroine tied to a small boat is drifting towards a waterfall at 3 m s−1. The small boat and heroine have a total mass of 200 kg.
(a) If the hero times his jumps perfectly so as to land on the small boat, and his velocity is 12 m s−1 at an angle of 80 º to the river current, what will be the velocity of the small boat immediately after his landing? Draw a vector diagram to show the momentum addition. Ignore any vertical motion.
(b) If the waterfall is 100 m downstream, and the hero landed when the small boat was 16 m from the bank, would they drop over the fall? Assume the velocity remains constant after the hero has landed. The small boat and the waterfall are on the same side of the bridge as he jumps.
A boy in a stationary boat on a still pond has lost his oars in the water. In order to get the boat moving again, he throws his rucksack horizontally out of the boat with a speed of 4 m s−1.
Mass of boat = 60 kg; mass of boy = 40 kg; mass of rucksack = 5 kg
(a) How fast will this action make the boat move?
(b) If he throws the rucksack by exerting a force on it for 0.2 s, how much force does he exert?
A movie stuntman with a mass of 90 kg stands on a stationary 1 kg skateboard. An actor throws a 3.4 kg brick at the stuntman who catches it. The brick is travelling at 4.1 m s−1 when caught.
A block of mass m is attached to a light spring with a spring constant k and located at its equilibrium position on a smooth horizontal surface. A damping force F(v) with a magnitude linearly proportional to speed v is also acting on the block.
a) Describe your system and sketch the free-body diagram (FBD) the block immediately after it is set in motion.
b) Write the equation of motion (EOM) for the particle and its general solutions.
c) Use relevant octave script to solve provided and plot the position and velocity of the block as a function of time.
d) Describe the state of motion of the particle based on the plots in part c).
below. The centre of the target is located 2.0 m below his hand.
Franz tosses the snowball with a velocity of 4.2 m/s at an angle of 50° above the
horizontal. The snowball hits the centre of the target, much to Franz’s delight. What is the horizontal distance between Franz and the target?
