Linear motion and projectiles – off a cliff

1.  A film stunt man dives of a cliff 20 m high, so that initially his vertical velocity is zero but his horizontal velocity is 5 ms-1. Find

a.  his vertical velocity as he hits the water

b.  the time taken

c.  the horizontal distance travelled during this time

2.  A stone is thrown horizontally from the top of a cliff with a speed of 5.6 ms-1. The cliff is 37 m high. Assuming that air resistance is negligible and that the acceleration of free fall is 9.81 ms-2, determine

a.  the time taken for the stone to fall to the bottom of the cliff

b.  the distance of the stone from the base of the cliff to where it lands

c.  the vertical component of the velocity of the stone when it lands

d.  the velocity of the stone when it lands

3.  A pencil is knocked horizontally off the edge of a desk at 2.0 ms-1. The desk is

65 cm high.

a.  how long does it take the pencil to reach the floor (ignore air resistance)

b.  what horizontal distance does the pencil travel during this time?

4.  An aid parcel is released from a plane flying horizontally at 60 ms-1. It is at a height of 1000m.

a.  What are the horizontal and vertical components or the parcel’s initial velocity?

b.  How long does the parcel take to hit the ground?

c.  At what horizontal distance should the plane be from its target when the parcel is released?

5.  A stone is projected horizontally from the top of a vertical sea cliff 49 m high, with a speed of 20 ms-1. Neglecting air resistance, calculate:

a.  The time that it takes for the stone the reach the sea

b.  The distance of the point of impact with the sea from the base of the cliff

c.  The velocity of the stone as it hits the sea

d.  Explain the effect that air resistance, if it was taken into account, would have on

a)  The time of flight

b)  The final velocity.

6.  At Acapulco, divers jump from a cliff 36 m high into the sea. At the base of the cliff there is a ledge which sticks out a distance of 6.4 m. What must be a diver’s minimum horizontal velocity if order to miss the ledge and enter the sea?