A projectile is fired at 12.5 m/s at an angle of 53.1 with the horizontal from a point 75m above the ground.
A) How long does it take to reach the ground?
B)What max height does it reach?
C) What horizontal distance does it travel before striking the ground?
D) With what velocity does it strike the ground?
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To solve these problems, we can use the equations of motion for projectile motion. Projectile motion is the motion of an object in a vertical and horizontal direction under the influence of gravity.
In this case, since we are given the initial velocity, angle, and initial height, we can use these values to find the answers.
A) To find how long it takes for the projectile to reach the ground, we need to find the time of flight. We can use the equation:
Time of flight (T) = 2 * (initial velocity * sin(angle)) / (acceleration due to gravity)
Here, the initial velocity is 12.5 m/s, the angle is 53.1 degrees, and the acceleration due to gravity is 9.8 m/s^2.
Therefore, substituting these values into the equation:
T = 2 * (12.5 m/s * sin(53.1 degrees)) / 9.8 m/s^2
Calculating this value will give you the time it takes to reach the ground.
B) To find the maximum height reached by the projectile, we can use the equation:
Maximum height (H) = (initial velocity * sin(angle))^2 / (2 * acceleration due to gravity)
Plugging in the values:
H = (12.5 m/s * sin(53.1 degrees))^2 / (2 * 9.8 m/s^2)
Evaluating this equation will give you the maximum height the projectile reaches.
C) To find the horizontal distance traveled before striking the ground, we can use the equation:
Horizontal distance (D) = initial velocity * cos(angle) * time of flight
Plugging in the values:
D = 12.5 m/s * cos(53.1 degrees) * T
Solving this equation will give you the horizontal distance traveled.
D) To find the velocity at which the projectile strikes the ground, we need to consider the horizontal and vertical components separately. The horizontal velocity remains constant throughout the motion, while the vertical velocity changes due to the effect of gravity.
The horizontal velocity (Vx) can be found using:
Vx = initial velocity * cos(angle)
Substituting the values:
Vx = 12.5 m/s * cos(53.1 degrees)
The vertical velocity (Vy) at the time of striking the ground can be found using:
Vy = initial velocity * sin(angle) - acceleration due to gravity * time of flight
Substituting the values:
Vy = 12.5 m/s * sin(53.1 degrees) - 9.8 m/s^2 * T
To find the resultant velocity (V) at which the projectile strikes the ground, we can use the Pythagorean theorem:
V = sqrt(Vx^2 + Vy^2)
Calculating this value will give you the velocity at which the projectile strikes the ground.
By following these steps, you can solve all the parts of the problem.