17 of 20 A student kicks a ball so that the ball\'s initial velocity is 8.3 m/s

Question

17 of 20 A student kicks a ball so that the ball's initial velocity is 8.3 m/s at 30°. How much time does the ball spend in the air? 1.7 s 1.3 s 1.2s 0.9 s 18 of 20 A student fires a bullet horizontally out of a gun. At the same time the bullet leaves the gun, the student drops a second bullet from the same height. Which bullet hits the ground first? The bullet fired from the gun will hit the ground first. The dropped bullet will hit the ground first The two bullets will hit the ground at the same time. The time depends on whether the bullets have the same mass.

Explanation / Answer

To find the time of flight, first, we need to determine the time the projectile takes to reach maximum height. The time of flight is just double the maximum-height time.

Start with the equation:

vy = voy + ay t

At maximum height, vy = 0.

The time to reach maximum height is t1/2 = - voy / ay

Time of flight is t = 2t1/2 = - 2voy / ay

Put in voy = vo sin(q) and ay = -g, gives:

Time of flight is t = 2 vo sin(q) / g

where g = 9.8 m/s2

The time of flight is also determined solely by the initial velocity in the y direction and the acceleration due to gravity.

t = 2*8.3*sin(300)

t= 8.3s.

18. The 2 bullets will hit at the same time.

reason: since you can treat Newton's second law and the resulting kinematics of uniformly accelerated motion separately for the horizontal and vertical components of the motion. you need to treat the air resistance as being zero and treat the Earth as flat, both of which we know not to be true.

However, in the real life, we should take into account the air resistance. The air resistance provides a drag force which is proportional to the square of the velocity and in the direction opposite to the velocity of the bullet. The vertical component of the air resistance for the fired bullet depends on the velocity of the bullet. That means we can’t treat horizontal motion and vertical motion as an independent. Therefore, the fired bullet does not hit the ground at the same time as the dropped bullet, the bullet fired horizontally will take a longer time to fall to the Earth.

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