a low velocity mortar round is fired upward at an angle of 50° from the horizontal with a launch velocity of 40 m/s
What is the question.?
Do they want to know the range?
R = (Vo^2/g)*sin(2A)
2A = 100 degrees
how long before it hits the ground!
Time of flight:
T = 2*Vo sinA/g
A = 50 degrees
It spends Vo sinA/g going up and an equal amount of time coming back down
To solve this problem, we can use basic kinematic equations of motion. Let's break down the information given:
Angle of Projection (θ): 50°
Launch Velocity (v₀): 40 m/s
Initial Velocity in the x-direction (v₀x): ?
Initial Velocity in the y-direction (v₀y): ?
To determine the initial velocities in the x and y directions, we can use trigonometry. The horizontal and vertical components of the initial velocity can be found using the following equations:
v₀x = v₀ * cos(θ)
v₀y = v₀ * sin(θ)
Substituting the values, we can calculate:
v₀x = 40 m/s * cos(50°) ≈ 40 m/s * 0.643 ≈ 25.72 m/s
v₀y = 40 m/s * sin(50°) ≈ 40 m/s * 0.766 ≈ 30.64 m/s
Now that we have the initial velocities in the x and y directions, we can determine various parameters related to the projectile motion.
1. Time of Flight (T):
The time it takes for the mortar round to reach the highest point and then return to the ground can be calculated using the formula:
T = 2 * v₀y / g
where g is the acceleration due to gravity (approximately 9.8 m/s²).
T = (2 * 30.64 m/s) / 9.8 m/s² ≈ 6.25 s
2. Maximum Height Reached (Hmax):
The maximum height can be determined using the equation:
Hmax = (v₀y)² / (2 * g)
Hmax = (30.64 m/s)² / (2 * 9.8 m/s²) ≈ 47.27 m
3. Horizontal Range (R):
The horizontal distance covered can be calculated using the equation:
R = v₀x * T
R = 25.72 m/s * 6.25 s ≈ 160.75 m
4. Impact Velocity:
The velocity of the mortar round upon impact can be calculated using the equation:
v_impact = sqrt((v₀x)² + (2 * g * Hmax))
v_impact = sqrt((25.72 m/s)² + (2 * 9.8 m/s² * 47.27 m)) ≈ 46.2 m/s
These calculations will give you the key parameters and values related to the motion of the low velocity mortar round fired at an angle of 50° from the horizontal with a launch velocity of 40 m/s.