If an object is thrown in an upward direction from the top of a building 1.60 x 102 ft. high at an initial velocity of 21.82 mi/h, what is its final velocity when it hits the ground? (Disregard wind resistance. Round answer to nearest whole number and do not reflect negative direction in your answer.)
this question is troubling me i guessed 96 ft/s
can someone help me out and explain it thanks so much
v₀ =21.82 mi/h, H= 1.60 x 102 ft.
Upward motion
h=v₀²/2g
Downward motion
H+h=v²/2g.
v=sqrt{2g(H+h)}
96ft/s
To solve this problem, we can use the equations of motion for projectiles.
First, let's convert the initial height and velocity to SI units for consistency.
- Initial height: 1.60 x 102 ft = 1.60 x 102 ft × 0.3048 m/ft = 48.768 m
- Initial velocity: 21.82 mi/h = 21.82 mi/h × 1609.34 m/mi ÷ 3600 s/h = 9.755 m/s
Now, let's use the equations of motion to find the time it takes for the object to hit the ground:
1. The equation for displacement in the vertical direction is given by:
Δy = V0y * t + (1/2) * g * t^2
where Δy is the vertical displacement, V0y is the initial vertical velocity, t is the time, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
2. Since the object is thrown upward, its final velocity when it hits the ground will be the negative of its initial velocity in the vertical direction:
Vfy = -V0y
3. The equation for vertical velocity is given by:
Vfy = V0y + g * t
Now, let's solve for time using the first equation. Since we are looking for the time it takes for the object to hit the ground, we set Δy equal to the negative of the initial height:
-48.768 = 9.755 * t + (1/2) * 9.8 * t^2
This is a quadratic equation, so we can solve it by either factoring or using the quadratic formula. After solving, we find that t ≈ 2.95 seconds.
Substituting the value of t into the third equation, we can find the final velocity when it hits the ground:
Vfy = 9.755 + 9.8 * 2.95 ≈ 35.15 m/s
Now, let's convert the final velocity back to feet per second:
35.15 m/s × 3.281 ft/m ≈ 115.30 ft/s
Lastly, round the answer to the nearest whole number as stated in the question, the final velocity is approximately 115 ft/s.