A 180 g arrow is shot straight up into the air
with a speed of 17 m/s. It reaches a maximum
height of 13.7449 m.
Find the initial kinetic energy. The accel-
eration of gravity is 9.8 m/s2 .
Answer in units of J.
max height means all initial KE has turned to pe
MaxPE=max Initial KE - friction loss
initial KE= 1/2 m v^2= 1/2 .180 *17^2=26joules
Final PE= m g h= .180*9.8*13.7449=24.246J
so, a small amount of energy was lost going up,probably to air friction.
Well, let's calculate the initial kinetic energy of this arrow.
The formula for kinetic energy is KE = (1/2) * m * v^2, where KE is the kinetic energy, m is the mass, and v is the velocity.
So, the initial kinetic energy would be (1/2) * 0.180 kg * (17 m/s)^2.
Let me do the math for you.
(1/2) * 0.180 * (17)^2 = 50.67 J.
Therefore, the initial kinetic energy of the arrow is approximately 50.67 Joules. Just remember, no clowning around with calculations!
To find the initial kinetic energy of the arrow, we can use the equation:
Kinetic energy = 1/2 * mass * velocity^2
Given:
Mass of the arrow (m) = 180 g = 0.18 kg
Velocity of the arrow (v) = 17 m/s
Substituting these values into the equation, we can calculate the initial kinetic energy:
Kinetic energy = 1/2 * 0.18 kg * (17 m/s)^2
Kinetic energy = 0.5 * 0.18 kg * 289 m^2/s^2
Kinetic energy = 26.01 J
Therefore, the initial kinetic energy of the arrow is 26.01 Joules.
To find the initial kinetic energy, we need to calculate the kinetic energy before the arrow is shot upward. The kinetic energy (KE) of an object can be calculated using the formula:
KE = 0.5 * mass * velocity^2
Here, the mass of the arrow is given as 180 g, which is 0.180 kg after converting to kilograms. The initial velocity is given as 17 m/s.
Plugging in these values into the formula, we get:
KE = 0.5 * (0.180 kg) * (17 m/s)^2
Calculating this expression, we get:
KE = 0.5 * 0.180 kg * (17 m/s)^2
= 0.5 * 0.180 kg * (289 m^2/s^2)
= 0.5 * 0.180 kg * 289 J
= 0.5 * 52.02 J
= 26.01 J
Therefore, the initial kinetic energy of the arrow is 26.01 Joules (J).