It is possible to shoot an arrow at a speed as high as 121 m/s.
(a) If friction is neglected, how high would an arrow launched at this speed rise if shot straight up?
No. Ultra light arrows with ultra strong bows can go almost 100m/s. Most hunting bows try for 200ft/sec, and most target bows are in the order of 100ft/sec. To get high speeds, the arrow weight is reduced more and more (think out why), and flight control is lost.
How high?
Vf^2=Vi^2 + 2g h
0=121^2-2*9.8h
h appx = 700m
To determine how high an arrow would rise if shot straight up at a speed of 121 m/s, we can use the principles of projectile motion.
The first step is to determine the initial velocity and acceleration of the arrow. Since the arrow is shot straight up, the initial velocity will be positive (upwards) and the initial acceleration will be negative due to gravity (-9.8 m/s^2).
Given:
Initial velocity (u) = +121 m/s
Acceleration (a) = -9.8 m/s^2
We can use the kinematic equation:
v^2 = u^2 + 2aΔy
Since the arrow is shot straight up, the final velocity (v) will be zero at the highest point. So the equation becomes:
0 = (121 m/s)^2 + 2(-9.8 m/s^2)Δy
Now we can solve for Δy (the change in height):
0 = 14641 m^2/s^2 - 19.6 m/s^2 Δy
Simplifying the equation:
19.6 m/s^2 Δy = 14641 m^2/s^2
Δy = 14641 m^2/s^2 / 19.6 m/s^2
Δy ≈ 746.6 m
Therefore, an arrow launched at a speed of 121 m/s would rise approximately 746.6 meters high if shot straight up, neglecting friction.