Question

1)A particle moves along the x axis. Its position is given by the equation

x = 1.8 + 2.5t − 3.9t² with x in meters and t in seconds.

(a) Determine its position when it changes direction.
(b) Determine its velocity when it returns to the position it had at t = 0? (Indicate the direction of the velocity with the sign of your answer.)

2)The height of a helicopter above the ground is given by h = 3.10t³, where h is in meters and t is in seconds. At t = 2.40 s, the helicopter releases a small mailbag. How long after its release does the mailbag reach the ground?

3)An inquisitive physics student and mountain climber climbs a 53.0-m-high cliff that overhangs a calm pool of water. He throws two stones vertically downward, 1.00 s apart, and observes that they cause a single splash. The first stone has an initial speed of 2.14 m/s.

(a) How long after release of the first stone do the two stones hit the water?
(b) What initial velocity must the second stone have if the two stones are to hit the water simultaneously?

magnitude

direction

(c) What is the speed of each stone at the instant the two stones hit the water?

first stone
second stone

Answer 1