A projectile is fired horizontally from a gun that is 97.0 m above flat ground, emerging from the gun with a speed of 250 m/s.
(a) How long does the projectile remain in the air?
s
(b) At what horizontal distance from the firing point does it strike the ground?
m
(c) What is the magnitude of the vertical component of its velocity as it strikes the ground?
m/s
Write equations of motion for the horizontal and vertical coordinates. Hasn't someone done that for you before?
(a) Solve the vertical motion equation for the time when the altitude is 0. The initial altitude is 97 m. The initial velocity will not matter in this case, since it is horizontal.
(b) X(final) = (initial velocity)*(time of flight)
(c) Add the change in potential energy to the initial kinetic energy, and get the final V from that.
Someone will be glad to critique your work. We will not do it for you.
a24
b16
c97
To solve this problem, we can use the equations of motion for a projectile launched horizontally. We can assume the acceleration in the horizontal direction is 0, and the acceleration in the vertical direction is equal to the acceleration due to gravity (approximately 9.8 m/s^2).
(a) To find the time of flight (how long the projectile remains in the air), we can use the equation:
time = distance / velocity
Since the distance in the horizontal direction is the same as the initial velocity, we have:
time = 250 m/s / 9.8 m/s^2
Solving this equation, we find:
time ≈ 25.5 s
Therefore, the projectile remains in the air for approximately 25.5 seconds.
(b) To find the horizontal distance the projectile travels before hitting the ground, we use the formula:
horizontal distance = velocity * time
Plugging in the values we know:
horizontal distance = 250 m/s * 25.5 s
Solving this equation, we find:
horizontal distance ≈ 6375 m
Therefore, the projectile strikes the ground at a horizontal distance of approximately 6375 meters from the firing point.
(c) To find the magnitude of the vertical component of the velocity when it strikes the ground, we can use the equation:
final velocity = initial velocity + acceleration * time
The initial vertical velocity is 0, and the final vertical velocity can be found using the equation:
final velocity = acceleration due to gravity * time
Plugging in the values, we have:
final velocity = 9.8 m/s^2 * 25.5 s
Solving this equation, we find:
final velocity ≈ 249.9 m/s
Therefore, the magnitude of the vertical component of the velocity as it strikes the ground is approximately 249.9 m/s.