To solve this problem, we can use the equations of motion for projectile motion. The time of flight and the range of the projectile can be determined based on the initial velocity, launch angle, and the vertical displacement.
Given: Launch angle (θ) = 35° Initial velocity (v₀) = 200 m/s Vertical displacement (Δy) = -300 m (negative because it lands below the launch point)
First, we can split the initial velocity into its horizontal and vertical components: v₀x = v₀ * cos(θ) v₀y = v₀ * sin(θ)
Time of flight (T): The time of flight is the total time taken for the projectile to reach the ground. The vertical motion is affected by gravity, so we can use the equation: Δy = v₀y * T + (1/2) * (-g) * T² Since the projectile lands at the same height as its initial position (Δy = 0), we can solve for the time of flight T.
0 = v₀ * sin(θ) * T + (1/2) * (-g) * T² 0 = 200 * sin(35°) * T + (1/2) * (-9.8) * T² 0 = 100 * T * sin(35°) - 4.9 * T²
Using this equation, we can solve for T. It is a quadratic equation, and we can use the quadratic formula to find the roots.
Range (R): The range is the horizontal distance covered by the projectile. We can use the horizontal motion equation: R = v₀x * T R = v₀ * cos(θ) * T
Using the values for v₀, cos(θ), and the time of flight T obtained from the previous calculations, we can find the range R.
Calculating the values will give you the specific time of flight and range of the projectile.