Assignment:
1. A certain freely falling object requires 1.10 s to travel the last 40.0 m before it hits the ground. From what height above the ground did it fall?
2. A student throws a set of keys vertically upward to his fraternity brother, who is in a window 4.05 m above. The brother's outstreched hand catches the keys 1.35 s later.
(a) With what initial velocity were the keys thrown?
(b) What was the velocity of the keys just before they were caught? (Take upward as the positive direction.)
3. A small mailbag is released from a helicopter that is descending steadily at 2.50 m/s.
(a) After 2.00 s, what is the speed of the mailbag?
(b) How far is it below the helicopter?
(c) What are your answers to parts (a) and (b) if the helicopter is rising steadily at 2.50 m/s?
4. A car starts from rest and travels for 7.0 s with a uniform acceleration of +2.5 m/s2. The driver then applies the brakes, causing a uniform acceleration of -2.0 m/s2. If the brakes are applied for 1.0 s, determine each of the following.
(a) How fast is the car going at the end of the braking period?
(b) How far has it gone?
5. 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 1000 m/s2 lasting for at least 1 ms will cause injury.
Suppose a small child rolls off a bed that is 0.41 m above the floor. If the floor is hardwood, the child's head is brought to rest in approximately 2.1 mm. If the floor is carpeted, this stopping distance is increased to about 1.0 cm. Calculate the magnitude and duration of the deceleration in both cases, to determine the risk of injury. Assume that the child remains horizontal during the fall to the floor. Note that a more complicated fall could result in a head velocity greater or less than the speed you calculate.