In the javelin throw at a track-and-field event, the javelin is launched at a speed of 29 m/s at an angle of 36???? above the horizontal. As the javelin travels upward, its velocity points above the horizontal at an angle that decreases as time passes. How much time is required for the angle to be reduced from 36???? at launch to 18?????

In the launch of projectiles, the velocity is broken down into its x and y components, the velocity in the x-axis is constant, as there is no acceleration, instead the velocity in the axis and is reduced by the effect of the acceleration of gravity.

We can find Vox for the initial conditions

Voy = Vo sin θ

Voy = 29 sin 36

VoY = 17 m/s

Vox = Vo cos θ

Vox = 29 cos 36

Vox= 23.5 m/s

Vx = Vox

The velocity on the x axis is constant

By trigonometry, we find the firing angle

tan θ = Voy/ Vx

Vy = Vx tan θ

Vy = 23.5 tan 18

Vy = 7.64 m/s

Now that we have the vertical speed we can find the time

Vy = I'm going - g t

t = (Vy -Voy) / g

t = (17 - 7.64) /9.8

t = 0.96 s

Be the time it takes for the angle to reduce