A spring-loaded toy gun is used to shoot a ball of mass m =1.50kg straight up in

Question

A spring-loaded toy gun is used to shoot a ball of massm=1.50kg straight up in the air, as shown in the figure. (Figure 1) The spring has spring constant k=667N/m. If the spring is compressed a distance of 25.0 centimeters from its equilibrium position y=0and then released, the ball reaches a maximum heighthmax (measured from the equilibrium position of the spring). There is no air resistance, and the ball never touches the inside of the gun. Assume that all movement occurs in a straight line up and down along the y axis.

Find vm the muzzle velocity of the ball (i.e., the velocity of the ball at the spring's equilibrium position y=0).??????

The following answer are incorrect

3.73

5.27

2.5

?3.73

1.41

Find the maximum height hmax of the ball.???????????

THe following are incorrect

.289m

3.73

Explanation / Answer

PE(spring) = 1/2kx^2
=>PE(s) = 1/2 x 667 x (0.25)^2
=>PE(s) = 20.84 J
=>By the law of energy conservation:-
=>PE(s) = KE(initial)
=>1/2mu^2 = 20.84
=>1/2 x 1.50 x u^2 = 20.84
=>u = ?27.79
=>u = 5.27 m/s

Again by the law of energy conservation:-
=>PE(final) = KE(initial)
=>mgh = 1/2mu^2
=>h = u^2/2g
=>h = 27.79/(2 x 9.8)
=>h = 1.42 m

answer = 5.27m/s and 1.42m

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