Question

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?????

Answer 1

The time required for a javelin's velocity angle to reduce from 36 degrees to 18 degrees in projectile motion can be found by comparing the initial and reduced vertical components of velocity and using kinematic equations.

Step-by-step explanation:

The question at hand is concerned with projectile motion and the change in the angle of a javelin's velocity with time. In projectile motion, the horizontal velocity component remains constant while the vertical component decreases due to gravity until it reaches zero at the apex of the trajectory. Afterward, the vertical component increases in the downward direction. As the javelin is thrown upwards, the vertical component (vy) decreases while the horizontal component (vx) remains the same. The angle (θ) of the velocity vector with the horizontal is given by the arctan(vy/vx).

To find the time when the angle reduces from 36 degrees to 18 degrees, we need to consider the vertical component of the motion. Initially, the vertical component of the velocity (vy) is v*sin(36°), and at the time when the angle is 18 degrees, it will be v*sin(18°). Assuming no air resistance and using the fact that the vertical velocity will decrease linearly due to acceleration due to gravity (g), we can set up an equation based on the kinematic equation vy = vy0 - g*t, where vy0 is the initial vertical component of the velocity and t is the time. By solving this equation, we can find the time t it takes for the angle to be reduced to 18 degrees.

Answer 2

t = 0.96 s is the time it takes for the angle to reduce

Step-by-step explanation:

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