Question

1. A small coin, initially at rest, begins falling. If the clock starts when the coin begins to fall, what is the magnitude of the coin's displacement between ?1=0.404 s and ?2=0.673 s?

Δ?=

2.

You attach a meter stick to an oak tree, such that the top of the meter stick is 1.67meters above the ground. Later, an acorn falls from somewhere higher up in the tree. If the acorn takes 0.121 seconds to pass the length of the meter stick, how high above the ground was the acorn before it fell, assuming that the acorn did not run into any branches or leaves on the way down?

3.

A small object begins a free-fall from a height of ?=85.0  m at ?0=0 s. After τ=2.40 s, a second small object is launched vertically up from the ground with an initial velocity of ?0=40.8 m/s. At what height from the ground will the two objects first meet?

height:

Answer 1

given,

t2 = 0.673 s ; t1 = 0.404 s

We know that, the displacement of falling object is given by:

D = 1/2 g t^2

for the given time range

D = 1/2 g (t2^2 - t1^2)

D = 0.5 x 9.81 x (0.673^2 - 0.404^2) = 1.421 m

Hence, D = 1.421 m

--------------------------------

2)avg velocity is:

v = L/t = 1/0.121 = 8.26 m/s

also v = 1/2 (vT + vB)

where vT and vB are the top and bottom velocity respectively

vB = vT + gt

vB = vT + 9.8 x 0.121 = vT + 1.19

putting this value of vB in abive eqn

8.26 = 0.5 (vT + vT + 1.19)

16.52 = 2vT + 1.19

vT = 7.67 m/s

vT^2 = 2 g h

h = vT^2/2g

h = 7.67^2/2 x 9.8 = 3 m

Hence, h = 3 m