Question

1. In a local bar, a customer slides an empty beer mug on the counter for a refill. The bartender does not see the mug, which slides off the counter and strikes the floor 1.40m from the base of the counter. If
the height of the counter is 0.860m.
a. With what speed did the mug
leave the counter.

b. What was the direction of the mug’s
velocity just before it hit the floor?

2. A projectile is launched from ground level with speed u at an angle of 
above the horizontal. Find in terms of u,
 and g by proving:

I. the maximum height H attained by the projectile,
II. the distance from the starting point at which the projectile strikes the ground; this is called the range R of the projectile.

Answer 1

1.

we have given range = 1.40 m

And height = 0.860 m

a) range =( velocity in x direction )× time of flight.....(1)

Time of flight = $\sqrt{2h\over g}= \sqrt{2×0.860\over 10}$ =0.29sec

Using (1)

1.40=speed ×0.29

Speed =4.8 m/s

b)

$V=u+gt$

$V=4.8+10×0.29$

$V=7.7 m/s$

2. Let angle be $\theta$

I)max height = $u^2sin^2(\theta)\over 2g$

ii)range = $ucos\theta ×{ 2usin\theta \over g}$