Question

A projectile is fired with a velocity of 45 m/s at an angle of 32 degrees. A box of mass 14 kg sits on an inclined surface with an angle of 52 degrees. What is the component of the weight of the box along the surface? What is the horizontal component of the velocity?

1) 45.0 m/s
2) 23.8 m/s
3) 38.2 m/s
4) 19.3 m/s

Answer 1

To find the component of the weight along the inclined surface, the formula W₁ = m⋅g⋅sin(θ) is used. The horizontal component of the projectile's velocity is found with the formula Vx = V⋅cos(α).

Step-by-step explanation:

To find the component of the weight of the box along the inclined surface, we use the formula W₁ = m⋅g⋅sin(θ), where m is the mass of the box, g is the acceleration due to gravity (9.8 m/s²), and θ is the angle of the inclined plane. In this case, m = 14 kg and θ = 52°. Therefore, W₁ = 14 kg ⋅ 9.8 m/s² ⋅ sin(52°), which we can calculate using a calculator.

For the horizontal component of the velocity of the projectile, we use the formula Vx = V⋅cos(α), where V is the initial velocity and α is the angle of projection. With V = 45 m/s and α = 32°, the horizontal component is Vx = 45 m/s ⋅ cos(32°), which can be evaluated using a calculator.