Question

A projectile is fired with an initial speed of 36.5m/s at an angle of 44.5 degrees above the horizontal on a long flat firing range. Determine the maximum height reached by the projectile Determine the total time in the air

Answer 1

The maximum height reached by the projectile is approximately 31.20 meters. The total time in the air is approximately 5.18 seconds.

Step-by-step explanation:

To determine the maximum height reached by the projectile, we can use the equation for vertical displacement:

Δy = (v₀y²) / (2g)

where Δy is the maximum height, v₀y is the initial vertical component of velocity, and g is the acceleration due to gravity.

Using the given values:

v₀ = 36.5 m/s

θ = 44.5°

we can find the vertical component of the initial velocity:

v₀y = v₀sinθ

v₀y = 36.5sin(44.5°)

v₀y ≈ 25.37 m/s

Substituting this value into the equation for vertical displacement:

Δy = (25.37²) / (2 * 9.8)

Δy ≈ 31.20 m

To determine the total time in the air, we can use the equation for total time of flight:

t = (2v₀y) / g

Substituting the given values:

t = (2 * 25.37) / 9.8

t ≈ 5.18 s