vneff said:Homework Statement
Assume there is a wall located 100m downrange (x=100) from the projectile launching position (x=0) that is 55m (y=55) high. What is the minimum initial velocity of the projectile launched at what angle necessary to clear the wall?
Homework Equations
h=(v^2sin^2α)/2g
The Attempt at a Solution
I can find the displacement but I'm confused as to how I am supposed to find both velocity and the projectile angle from this information.
Do exactly what azizlwl said. You have two unknowns, so you need two equations to get a solution. You could find one of those equations by considering energy and the other by using projectile kinematics.vneff said:Homework Statement
Assume there is a wall located 100m downrange (x=100) from the projectile launching position (x=0) that is 55m (y=55) high. What is the minimum initial velocity of the projectile launched at what angle necessary to clear the wall?
Homework Equations
h=(v^2sin^2α)/2g
The Attempt at a Solution
I can find the displacement but I'm confused as to how I am supposed to find both velocity and the projectile angle from this information.
The minimum initial velocity needed to launch a projectile at a certain angle depends on various factors such as the angle of launch, the mass of the projectile, and the force of gravity. However, in a vacuum with no air resistance, the minimum initial velocity can be calculated using the equation Vmin = √(g * d / sin(2θ)), where g is the acceleration due to gravity, d is the horizontal distance the projectile needs to cover, and θ is the launch angle.
The angle of launch has a significant effect on the minimum initial velocity of a projectile. As the launch angle increases, the minimum initial velocity needed to reach a certain distance decreases. This is because at a higher angle, the vertical component of the initial velocity is smaller, allowing the projectile to travel a longer horizontal distance with the same initial velocity.
Yes, the minimum initial velocity of a projectile can be calculated without considering air resistance. In a vacuum, the only force acting on the projectile is the force of gravity, and the minimum initial velocity can be calculated using the equation Vmin = √(g * d / sin(2θ)). However, in real-world scenarios, air resistance must be taken into account, and the minimum initial velocity will be higher due to the resistance force.
The mass of a projectile has a direct impact on the minimum initial velocity. The greater the mass of the projectile, the higher the minimum initial velocity needed to launch it at a certain angle and reach a specific distance. This is because a heavier projectile requires more force to overcome its inertia and travel a certain distance.
No, the minimum initial velocity of a projectile cannot be greater than its escape velocity. The escape velocity is the minimum velocity needed for an object to overcome the gravitational pull of a planet or celestial body and escape its orbit. Therefore, the minimum initial velocity needed to launch a projectile at a certain angle will always be lower than its escape velocity.