a ball of mass 0.1kg is thrown vertically upwards with an initial velocity of 80m/s.calculate the potential energy (I) half way up (ii) at its maximum height.what is the kinetic energy as it leaves the ground
at max ht v=0
therfore u^2=2gh
h=u^2/2g
for halway do h\2
time
hw did u get u max height? i did not understand
To calculate the potential energy (PE) of the ball at different points during its motion, we need to consider its position and mass. The potential energy is given by the formula PE = mgh, where m is the mass of the ball, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height or distance from a reference point.
(i) Halfway up:
To find the potential energy halfway up, we need to determine the height at that point. Assuming upward motion, the ball will lose its initial velocity due to gravity. At the halfway point, its velocity will be zero before it starts descending. Using the kinematic equation v² = u² + 2as, where v is the final velocity, u is the initial velocity, a is acceleration, and s is displacement, we can solve for the displacement.
At the peak, the final velocity is zero (v = 0), the initial velocity is 80 m/s (u = 80 m/s), and the acceleration is -9.8 m/s² (negative because it is acting in the opposite direction). Plugging these values into the equation, we get:
0² = 80² + 2(-9.8)s
0 = 6400 - 19.6s
-19.6s = -6400
s = 326.53 m
Halfway up, the ball has traveled 326.53 meters. Now we can calculate the potential energy using the formula:
PE = mgh
PE = 0.1 kg * 9.8 m/s² * 326.53 m
PE ≈ 321.51 Joules
(ii) At its maximum height:
At the maximum height, the ball comes to rest before it begins to descend. The potential energy can be calculated using the formula PE = mgh, where h is the maximum height reached by the ball.
Using the same method as before, we can determine the distance traveled to reach the maximum height:
v² = u² + 2as
0² = 80² + 2(-9.8)s
-6400 = -19.6s
s ≈ 326.53 m
The maximum height is equal to the displacement, which is 326.53 meters. Now we can calculate the potential energy:
PE = mgh
PE = 0.1 kg * 9.8 m/s² * 326.53 m
PE ≈ 321.51 Joules
The potential energy halfway up and at the maximum height is approximately 321.51 Joules.
To calculate the kinetic energy (KE) as the ball leaves the ground, we can use the formula KE = 1/2 mv², where m is the mass of the object and v is the velocity.
Given:
Mass (m) = 0.1 kg
Initial velocity (u) = 80 m/s
KE = 1/2 * 0.1 kg * (80 m/s)²
KE = 0.5 * 0.1 kg * 6400 m²/s²
KE = 0.5 * 640 Joules
KE = 320 Joules
The kinetic energy as the ball leaves the ground is 320 Joules.
V^2 = Vo^2 + 2g*h = 0, h = -Vo^2/2g = -80/-19.6 = 4.08 m. =
max. ht.
1. PE = M*g*h/2 = 0.1*9.8*(4.08/2) = 2.0 Joules.
2. PE = 0.1*9.8*4.08 = 4.0 Joules.
3. KE = 0.5M*V^2 = 0.5*0.1*80^2 = 320 Joules.