Answer to Question #253360 in Mechanics | Relativity for secret

Question

In a carnival booth, you win a stuffed giraffe if you toss a quarter into a small dish. The dish is on a shelf above the point where the quarter leaves your hand and is a horizontal distance of 2.1 m from this point. If you toss the coin with a velocity of at an angle of above the horizontal, the coin lands in the dish. You can ignore air resistance.

(a) What is the height of the shelf above the point where the quarter leaves your hand?

(b) What is the vertical component of the velocity of the quarter just before it lands in the

dish?

Answer 1

a)

$l'=\frac{v^2\sin2\alpha}{2g}=1.81~m,$

$\Delta l=l-l'=0.29~m,$

$t=\frac{\Delta l}{v\cos \alpha}=0.09~s,$

$h=\frac{gt^2}2=0.04~m,$

$h'=\frac{v^2\sin^2\alpha}{2g}=1.57~m,$

$\Delta h=h'-h=1.53~m,$

b)

$v_y=gt=0.88~\frac ms.$