A 90g arrow is shot straight up into the air with a spped of 23 m/s. It reaches a maximum height of 25.9898m. Find the initial kinetic energy. the acceleration of gravity is 9.8 m/s2. Answer in units of J. Find the potential energy at its highest position. Answer in units of J.
Use the formulas for kinetic energy:
(1/2) M V^2, and
potential energy:
(M g H)
They should give you the same answer, except for possible differences in rounding.
To find the initial kinetic energy of the arrow, we can use the formula:
Kinetic Energy (KE) = 1/2 * mass * velocity^2
Given:
Mass (m) = 90g = 0.09 kg
Velocity (v) = 23 m/s
Substituting the values into the formula:
KE = 1/2 * 0.09 kg * (23 m/s)^2
KE = 0.5 * 0.09 kg * (529 m^2/s^2)
KE = 13.365 J (rounded to three decimal places)
Therefore, the initial kinetic energy of the arrow is approximately 13.365 J.
To find the potential energy at its highest position, we can use the formula:
Potential Energy (PE) = mass * acceleration due to gravity * height
Given:
Mass (m) = 90g = 0.09 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Height (h) = 25.9898 m
Substituting the values into the formula:
PE = 0.09 kg * 9.8 m/s^2 * 25.9898 m
PE = 22.5393 J (rounded to four decimal places)
Therefore, the potential energy at the highest position of the arrow is approximately 22.5393 J.