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Good Day

problem:

a ball is thrown upward with a velocity of 30 m/s . solve for the following ? A.time to reach the maximum height B. maximum Height reached C. time until the ball returns to its origin D.velocity with which the ball returns to its origin

A.time to reach the maximum height (time = 3.06 s)

Given:

Vi (initial velocity) = 30 m/s

a (acceleration) = -9.8 m/s² (decelerating)

Vf (final velocity) = 0 m/s (at maximum height)

t (time) = ?

Solution:

t = Vf-Vi/a

= 0 m/s - 30 m/s / -9.8 m/s²

= -30 m/s / -9.8 m/s²

time = 3.06 s

B. maximum Height reached ( = 45.9 meters)

Vi (initial velocity) = 30 m/s

a (acceleration) = -9.8 m/s² (decelerating)

Vf (final velocity) = 0 m/s (at maximum height)

t (time) = 3.06 s

d (distance) = unknown

Solution:

d = (Vf+Vi)/2 × t

= 0 m/s + 30 m/s / 2 × 3.06 s

= 15 m/s × 3.06 s

= 45.9 m

C. time until the ball returns to its origin6.12 seconds

3.06 s going up and the same time for the ball from top going to the same elevation where it start so the

total time 3.06 s up + 3.06 s down = 6.12 seconds

D.velocity with which the ball returns to its origin (30 m/s)

the initial velocity from where it start is the same velocity as the ball returns to same elevation.

Hello!

A car with a mass of 1200 kg is travelling at a constant speed of 40 m/s. what is the car's kinetic energy?

We have the following data:

m (mass) = 1200 kg

v (velocity) = 40 m/s

KE (kinetic Energy) = ? (in Joule)

Formula to calculate kinetic energy:

Solving:

_______________________

#BrainlySummerChallenge

a. Jane's initial speed is 2.45 m/s

b. The change in kinetic energy is 291 J

Explanation:

Here, we are to solve for the initial speed of Jane and the change of kinetic energy due to her change in speed.

For the formula, we will use:

a. KE = ¹/₂mv²

b. ΔKE = KE₂ - KE₁

where

KE is the kinetic energy, unit is in Joules (J)

m is the mass, unit is in kg

v is the speed, unit is in m/s

For the given information

KE₁ = 150 J

v₂ = 4.2 m/s

m = 50 kg

a. v₁ = ?

b. ΔKE = ?

Solving the problem

a. First, let us solve for the initial speed, v₁ of Jane while she was walking. Let us use the first given formula, we have:

KE = ¹/₂mv²

Let us assign the variables as the initial kinetic energy then substitute the given information, we have:

KE₁ = ¹/₂mv₁²

150 J = ¹/₂(50 kg) v₁²

Cross - multiply

v₁ =

v₁ = 2.45 m/s

b. Now, let us solve for the final kinetic energy when Jane starts running. Let us use the formula:

KE₂ = ¹/₂mv₂²

KE₂ = ¹/₂(50 kg) (4.2 m/s)²

KE₂ = 441 J

c. Now, we are ready to solve for the change in kinetic energy, let us use the second given formula, we have:

ΔKE = KE₂ - KE₁

Then, substitute the given information, we have:

ΔKE = 441 J - 150 J

ΔKE = 291 J

Therefore, the initial speed of Jane while she was walking is 2.45 m/s and the change in kinetic energy due to change to her speed is 291 J.

To learn more, just click the following links:

Definition of kinetic energyExamples of kinetic energy

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