PHYS 2211 Module 4 Self Assessment Practice Problems

Module 4 Self Assessment Practice Problems

4.1
The position of a particle is m.
(a) Determine its velocity and acceleration as functions of time.
(b) What are its velocity and acceleration at time t = 0?
Answer: (a) m/s, (b) m/s, m/s2 (Click and drag over the answer to highlight it)
4.2
A boat leaves the dock at t = 0 and heads out into a lake with an acceleration of . A strong wind is pushing the boat, giving it an additional velocity of .
(a) What is the velocity of the boat at t = 10 s?
(b) What is the position of the boat at t = 10 s?
(c) Draw a sketch of the boat’s trajectory and position at t = 10 s, showing the x– and y-axes.
Answer: (a) (b)
4.3
A marble rolls off a tabletop 1.0 m high and hits the floor at a point 3.0 m away from the table’s edge in the horizontal direction.
(a) How long is the marble in the air?
(b) What is the speed of the marble when it leaves the table’s edge?
(c) What is its speed when it hits the floor?
Answer: (a) 0.45 s, (b) 6.64 m/s, (c) 8 m/s
4.4

An airplane flying horizontally with a speed of 500 km/h at a height of 800 m drops a crate of supplies (see the figure). If the parachute fails to open, how far in front of the release point does the crate hit the ground?
Answer: 1779 m
4.5
At a particular instant, a hot air balloon is 100 m in the air and descending at a constant speed of 2.0 m/s. At this exact instant, a girl throws a ball horizontally, relative to herself, with an initial speed of 20 m/s. When she lands, where will she find the ball? Ignore air resistance.
Answer: 86.0 m
4.6
A rock is thrown off a cliff at an angle of 53° with respect to the horizontal. The cliff is 100 m high. The initial speed of the rock is 30 m/s.
(a) How high above the edge of the cliff does the rock rise?
(b) How far has it moved horizontally when it is at maximum altitude?
(c) How long after the release does it hit the ground?
(d) What is the range of the rock?
Answer: (a) 29.3 m, (b) 43.2 m, (c) 7.58 s, (d) 136.4 m
4.7
MIT’s robot cheetah can jump over obstacles 46 cm high and has speed of 12.0 km/h.
(a) If the robot launches itself at an angle of 60° at this speed, what is its maximum height?
(b) What would the launch angle have to be to reach a height of 46 cm?
Answer: (a) 0.43 m, (b) 65.5°
4.8
The Lunar Roving Vehicle used in NASA’s late Apollo missions reached an unofficial lunar land speed of 5.0 m/s by astronaut Eugene Cernan. If the rover was moving at this speed on a flat lunar surface and hit a small bump that projected it off the surface at an angle of 20°, how long would it be “airborne” on the Moon?
Answer: 2.1 s
4.9
A fairground ride spins its occupants inside a flying saucer-shaped container. If the horizontal circular path the riders follow has an 8.00-m radius, at how many revolutions per minute are the riders subjected to a centripetal acceleration equal to that of gravity?
Answer: 10.6 rev/min
4.10
A runner taking part in the 200-m dash must run around the end of a track that has a circular arc with a
radius of curvature of 30.0 m. The runner starts the race at a constant speed. If she completes the 200-m dash in 23.2 s and runs at constant speed throughout the race, what is her centripetal acceleration as she runs the curved portion of the track?
Answer: 2.5 m/s2