Mechanics | Relativity Answers

1.   One morning, while little Lenlen’s mother was busy in the kitchen, Little Lenlen rolls off the bed that is 0.50 m above the floor. If the floor is hardwood, little Lenlen’s head is brought to rest in approx. 2.0 mm. If the floor is carpeted, this stopping distance is increased to about 1.0 cm. Calculate the magnitude and duration of the acceleration in both cases, to determine the risk of injury. Assume that little Lenlen remains horizontal during the fall to the floor. (Note: A more complicated fall could result in a head velocity greater or less than the speed you calculate. Traumatic brain injury such as concussion results when the head undergoes a very large acceleration. Generally, an acceleration less than 800 m/s² lasting for any length of time will not cause injury, whereas an acceleration greater than 1000m/s² lasting for at least 1 ms will cause injury.)

1.     A summersault swimmer stands on a high platform jumps vertically upward with a velocity of magnitude 2.5 m/s. Air resistance maybe ignored.

a.)   At what time after moving from the platform does the swimmer have a velocity of 0.25 m/s upward?

b.)   At what time does she has a velocity of 0.25 m/s downward?

c.)   When is the displacement of the swimmer from its initial position zero?

d.)   When is the velocity of the swimmer zero?

e.)   What are the magnitude and direction of the acceleration while the swimmer is

i.)                Moving upward?  

ii.)              Moving downward?

Tom, the cat, and Jerry, the mouse enter a race over a course of 1.00 km long. Jerry sprints to its maximum speed of 3.34 m/s toward the finish line. Tom runs also at its maximum speed of 13.33 m/s toward the goal for 0.800 km and then stops to tease Jerry. How close to the goal can Tom let Jerry approach before resuming the race, which Jerry wins in the race? 

You are standing on the sci.com. building 46.0 m high above the ground. Your classmate, 1.8 m tall, is walking alongside the building at a constant speed of 1.20 m/s. If you wish to drop an egg onto his head,

a) where should he be when you release the egg? Assume that the egg is in free fall.

b) what will be the velocity of the egg when it hits his head?

A car heading east through a city accelerates after passing a signpost marking the city limits. It is accelerating at

constant magnitude of 3.0 m/s2. At time t = 0 the car is 5.0 m east of the signpost, moving east at 15 m/s. a) Find the car’s position at t=2.0 s.

b) Find the car’s velocity at t=2.0 s.

c) Where is the car when its velocity is 25 m/s.

If a student jumps straight up to a height of 0.440m, what is his initial speed as it leaves the ground? How long

is he in the air?

A car is stopped at the traffic light. It then travels along a straight road so that its distance from the light is given by 𝑥(𝑡) = 𝑏𝑡2 − 𝑐𝑡3 where b=2.40 m/s2 and c=0.120 m/s3.

a) Calculate the average velocity of the car for the time interval t=0 to t=10.0 s.

b) Calculate the instantaneous velocity of the car at t=0 and t=10.0s

c) How long after starting again from rest is the car again at rest.

Find the tension in the horizontal part of the supporting cable, and the compression in the boom, elevated to 25.0°, of the crane that lifts a 8900.N load.

A boy moves from point A in distance 20m in the direction North 60° East to arrive at point B in a direction North 30° East for point C,10m away from point B.What is it vector location from point A?

A small sphere of charge +6×10^-6 C is suspended by a string of negligible mass. A charge of -9.0×10^-6 C is placed directly to the right of the sphere and 0.22m away from it. The string is deflected 5^0 from the vertical. Find the tension in the string.