an arrow is shot vertically upward 2 seconds later it is at a height of 42m (this may not be necesarily its highest point)with what velocity was the arrow shot, how long is the arrow in flight altogether
v = Vi - 9.81 t
h = Hi + Vi t - 4.9 t^2
42 = 0 + Vi(2) - 4.9(4)
Vi = 30.8 meters/ second
when it hits ground, v = -30.8 m/s
v = Vi - 9.81 t
-30.8 = 30.8 - 9.81 t
t = 6.28 seconds
To determine the initial velocity of the arrow and the total time in flight, we can use the laws of motion and the given information.
Let's assume that the acceleration due to gravity is approximately 9.8 m/s² (neglecting air resistance).
1. Find the initial velocity of the arrow:
Since the arrow is shot vertically upward, its final velocity at its highest point would be zero. We can use the second equation of motion:
v_f = v_i + at
Here, v_f is the final velocity (zero), v_i is the initial velocity (what we're trying to find), a is the acceleration due to gravity (-9.8 m/s²), and t is the time taken (2 seconds).
Substituting the values into the equation:
0 = v_i + (-9.8 m/s²) * 2 s
Simplifying the equation:
v_i = 9.8 m/s² * 2 s
v_i = 19.6 m/s
Therefore, the arrow was shot vertically upward with an initial velocity of 19.6 m/s.
2. Find the total time in flight:
To find the total time in flight, we need to consider both the ascent and descent of the arrow.
During the ascent, the initial velocity is 19.6 m/s, and the final velocity is zero when the arrow reaches its highest point. Using the first equation of motion:
v_f = v_i + at
0 = 19.6 m/s + (-9.8 m/s²) * t₁
Simplifying the equation:
t₁ = 19.6 m/s / 9.8 m/s²
t₁ = 2 s
During the descent, we can use the same equation of motion, but this time the initial velocity is zero, and the final velocity is unknown. Let's call the time taken during the descent as t₂.
v_f = v_i + at
0 = 0 m/s + (-9.8 m/s²) * t₂
Simplifying the equation:
t₂ = 0 / (-9.8 m/s²)
t₂ = 0 s
Since the arrow is at a height of 42 m after 2 seconds, it implies that the total time in flight is 2 seconds (t₁ = ascent time + t₂ = descent time).
Therefore, the arrow is in flight for a total of 2 seconds, and it was shot with an initial velocity of 19.6 m/s.