A projectile fired with an know initial velocity lands 20s later on the side of a hill 3000m away horizontally and 450m vertically above its strating point . Find the horizontal and vertical components of its initial velocity
To find the horizontal and vertical components of the initial velocity of the projectile, we can use the information given: the time of flight (20s), the horizontal distance (3000m), and the vertical displacement (450m).
The horizontal component of the initial velocity remains constant throughout the projectile's motion. So, we can use the formula:
Horizontal distance = Horizontal velocity × Time of flight
Given that the horizontal distance is 3000m and the time of flight is 20s, we can rearrange the formula to solve for the horizontal velocity:
Horizontal velocity = Horizontal distance / Time of flight
= 3000m / 20s
= 150 m/s
Therefore, the horizontal component of the initial velocity is 150 m/s.
The vertical component of the initial velocity is affected by gravity. We can use the formula for vertical displacement:
Vertical displacement = (Initial vertical velocity × Time of flight) + (0.5 × Acceleration due to gravity × Time of flight^2)
Given that the vertical displacement is 450m and the time of flight is 20s, we need to determine the initial vertical velocity. The acceleration due to gravity is approximately 9.8 m/s^2.
450m = (Initial vertical velocity × 20s) + (0.5 × 9.8 m/s^2 × 20s^2)
450m = 20s × (Initial vertical velocity + 10s × 9.8 m/s^2)
450m - 20s × 10s × 9.8 m/s^2 = 20s × Initial vertical velocity
450m - 1960m = 20s × Initial vertical velocity
-1510m = 20s × Initial vertical velocity
Initial vertical velocity = -1510m / 20s
Initial vertical velocity = -75.5 m/s
Therefore, the vertical component of the initial velocity is -75.5 m/s.
In conclusion, the horizontal component of the initial velocity is 150 m/s, and the vertical component of the initial velocity is -75.5 m/s.
horizontal velocity is constant ... v = 3000 m / 20 s
vertical velocity is subject to gravitational acceleration
... 450 m = [-1/2 * g * (20 s)^2] + (v * 20 s)