PHYSICS

Answered question

2021-10-28

3.19 Win the Prize. In a carnival booth, you can 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 (Fig. E3.19). If you toss the coin with a velocity of 6.4 m/s at an angle of 60° above the horizontal, the coin will land in the dish. Ignore air resistance. (a) What is the height of the shelf above the point where the quar ter leaves your hand? (b) What is the vertical component of the velocity of the quarter just before it lands in the dish?

Answer & Explanation

Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-02Added 2605 answers

(a)

The vertical displacement of the quarter to reach the shelf from the hand is,

y=uyt12gt2

Here, uy is the vertical component of initial velocity of the quarter, g is the acceleration due to gravity and tt is the time.

Substitute 5.5m/s  for uy​, 9.8m/s2 for g and 0.66 s for time  to find the vertical displacement of the quarter.

y=(5.5 m/s)(0.66 s)12(9.8 m/s2)(0.66 s)2

=1.5 m

The height of shelf from the point the quarter left the hand is 1.5m.

(b)

The vertical component of initial velocity of the quarter is,

uy=usinθ

Substitute 6.4m/s for u and 60for θ.

 

uy=(6.4 m/s)(sin60)

=5.5 m/s

The horizontal component of initial velocity of the quarter is,

ux=ucosθ

Substitute 6.4m/s for u and 60 for θ.

uy=(6.4 m/s)(cos60)

=3.2 m/s

There are two components to the initial velocity of the quarter which keeps the quarter in two dimensional projectile motion.

The time taken by the quarter to reach the dish is,

t=xvx

Substitute 2.1m for x and 3.2m/s for vx.

t=2.1 m3.2 m/s

=0.66 s

The time taken by the projectile to reach the dish is the ratio of the displacement to the horizontal velocity of the projectile.

The vertical component of the final velocity of the quarter is,

vy=uygt

Substitute 5.5m/s for uy9.8m/s2 for g and 0.66 s for time tt to find the vertical component of the velocity.

vy=(5.5 m/s)(9.8 m/s2)(0.66 s)

=0.93 m/s

The vertical component of the velocity of the quarter just before it lands in the dish is 0.93 m/s

The vertical velocity of the quarter changes with time and it depends on the vertical component of initial velocity, time and acceleration due to gravity. When the projectile moves upwards, the acceleration acts downwards.

 

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