To determine the time taken by the bomb to reach the highest point, we can analyze the vertical motion of the projectile.
Given: Initial velocity (v₀) = 1,000 m/s Launch angle (θ) = 30 degrees
First, we can decompose the initial velocity into its horizontal and vertical components:
Vertical component (v₀y) = v₀ * sin(θ) Horizontal component (v₀x) = v₀ * cos(θ)
At the highest point of the projectile's trajectory, the vertical velocity becomes zero. Using this information, we can calculate the time taken to reach the highest point.
The equation for vertical motion is:
v_y = v₀y - g * t
where v_y = vertical velocity at time t v₀y = initial vertical velocity g = acceleration due to gravity (approximately 9.8 m/s²) t = time
At the highest point, v_y = 0. Therefore, we can rewrite the equation as:
0 = v₀y - g * t
Solving for time:
g * t = v₀y
t = v₀y / g
Substituting the values:
v₀y = v₀ * sin(θ) g = 9.8 m/s²
t = (v₀ * sin(θ)) / g
t = (1,000 m/s * sin(30°)) / 9.8 m/s²
Using the values of sin(30°) = 0.5:
t = (1,000 m/s * 0.5) / 9.8 m/s²
t ≈ 51.02 seconds
Therefore, the time taken by the bomb to reach the highest point is approximately 51.02 seconds.