Question

A projectile is launched at an angle of 30 degrees, relative to the horizontal, with a velocity of 50 m/s. Increasing the launch angle will ________________ the vertical component of the initial velocity. Increasing the launch angle will __________________ the time the projectile spends in the air.

Answer 1

Answer:

both will increase

Explanation:

vertical component velocity of the body = 50 sin 30⁰ = 25 m/s

let say the angle was increase to 45⁰ and the velocity did not change

vertical component of the velocity = 50 sin 45⁰ = 35 m/s

change again to 60⁰

vertical component of the velocity = 50 sin 60⁰ = 43.3 m/s

the vertical component of the velocity will continue to increase until the angle is 90⁰⁰ at which the vertical component of the velocity will be equal to the velocity of projection and the horizontal component will be zero.

Similarly the time also will increase as the angle increases

take the equation of motion

h = ut + 1/2gt²

total displacement is zero since it goes up and return to the ground

0 = ut -g1/2gt ²

-2ut = - gt²

where u is the vertical component of the velocity and becomes u sin 30

2u sin 30 = gt

t = $\frac{2u sin 30}{g}$

t is directly proportional to sin θ where θ is the angle of projection

until theta is 90.