Question

Suppose the airplane in the preceding problem fires a projectile horizontally in its direction of motion at a speed of 300 m/s relative to the plane. (a) How far in front of the release point does the projectile hit the ground? (b) What is its speed when it hits the ground?

Answer 1

a) s = 5619.2 m

b) v = 456.5 m/s

Note: The preceding question is given below:

An airplane flying horizontally with a speed of 500 km/h at a height of 800 m drops a crate of supplies (see the following figure). If the parachute fails to open, how far in front of the release point does the crate hit the ground?

Step-by-step explanation:

From the preceding question;

height, h = 800 m,

speed of plane = 500 km/h = 500000 m / 3600 s = 139 m/s

Speed of projectile = 139 m/s + 300 m/s = 439 m/s

a) using h = ut + 1/2 * gt² = 1/2 gt² (sice u = 0)

t = √(2h/g) where g = 9.8 m/s²

t = √(2 * 800/9.8)

t = 12. 8 s

horizontal distance, s = horizontal velocity * time

s = 439 * 12.8

s = 5619.2 m

b) Final vertical velocity v₂ = u - gt

v₂ = 0 - 9.8 * 12.8 = 125.4 m/s

horizontal velocity, vₓ = 439.0 m/s

resultant velocity, v = √(v₁² + vₓ²)

v = √{(125.4)² + (439.0)²}

v = 456.5 m/s