Damon
answered
F = -mg
so a = -g = -9.8
v = Vo -9.8t
0 at top = 20 - 9.8 t
t at top = 20/9.8 (same time falling so double that for time in air)
at t = t at top. how high is it?
h = 20 t - (1/2) (9.8) t^2
Jake
answered
For the rise I do not multiply by 2 t right? I got answer of 20.4
I am very glad that you were able to help me with this problem
Step-by-Step Bot
answered
t = (2 * v) / g
where t is the time, v is the initial velocity, and g is the acceleration due to gravity (approximately 9.8 m/s²).
Substituting the given values, we have:
t = (2 * 20 m/s) / 9.8 m/s²
t = 2.04 seconds
Therefore, the arrow is in the air for approximately 2.04 seconds.
To find the maximum height the arrow will reach, we can use the equation:
h = (v²) / (2 * g)
where h is the maximum height.
Substituting the given values, we have:
h = (20 m/s)² / (2 * 9.8 m/s²)
h = 204 / 19.6
h ≈ 10.41 meters
Therefore, the arrow will rise to a maximum height of approximately 10.41 meters.
Explain Bot
answered
The time it takes for the arrow to reach its highest point can be found using the equation for vertical motion:
v(final) = v(initial) + (acceleration * t),
where v(final) is the final velocity, v(initial) is the initial velocity, acceleration is the acceleration due to gravity (approximated as 9.8 m/s²), and t is the time taken.
In this case, we have:
0 m/s = 20 m/s + (-9.8 m/s² * t).
By rearranging the equation, we can solve for t:
-20 m/s = -9.8 m/s² * t.
Dividing both sides of the equation by -9.8 m/s² yields:
t = 20 m/s / 9.8 m/s²,
t ≈ 2.04 seconds.
So, the arrow will be in the air for approximately 2.04 seconds.
To determine how high the arrow will rise, we can use the equation for vertical displacement during uniform acceleration:
s = v(initial) * t + (1/2) * acceleration * t²,
where s is the displacement (height), v(initial) is the initial velocity, acceleration is the acceleration due to gravity, and t is the time taken.
Plugging in the given values:
s = 20 m/s * 2.04 s + (1/2) * (-9.8 m/s²) * (2.04 s)²,
s ≈ 20.4 m.
Therefore, the arrow will rise to a height of approximately 20.4 meters.
