Helen Lewis

2022-01-05

A coin is dropped from a hot-air balloon that is 300 m above the ground and rising at 10.0 m/s upward. For the coin, find (a) the maximum height reached, (b) its position and velocity 4.00 s after being released, and (c) the time before it hits the ground.

Robert Pina

Beginner2022-01-06Added 42 answers

Step 1

According to kinematic equation the final velocity is given by

1)

Where it is given that:

(1) The max point so the final velocity

(2) The acceleration is

(3) The initial displacement

So substitution in (1) yields

Step 2

The displacement y is given by

2)

Where it is given that:

(1) The times

(2) The acceleration

(3) The initial velocity

(4) The initial displacement

So substitution in (2) yields

Which means that the coin is falling down.

Step 3

The time taken before hitting the land is given by equation (2) where it is given that

(1) The final velocity

(2) The acceleration

(3) The initial velocity

(4) The initial displacement

So substitution in (2) yields

Solving (3) for t and get the positive root

godsrvnt0706

Beginner2022-01-07Added 31 answers

Step 1

General formula for position is:

Where

Step 2

a) To find maximum height reached, one can derive

Extremum of function demands first derivative to be equal to zero, thus:

Maximum height will be reached at

Step 3

b) Velocity after 4.00 s after release can be calculated as follows:

negative sign means coin is travels downwards. Position after 4.00 s after release:

above the ground.

Step 4

c) Coin hitting the ground means it’s position is 0 m. To get time, one can solve the equation:

There are two roots, one of which is negative – but because time can’t be negative, that root is not physical one, so it’s neglected. The one that’s left:

karton

Expert2022-01-10Added 613 answers

Step 1

Initial position:

Initial velocity:

Gravity's acceleration:

a) From Kinematics:

When the coin reaches it's maximum height, it's velocity will be

Maximum height will be

Step 2

b) From Kinematics, the movement law will be:

where

At t=4s

c) Again, we have that:

Now, if y final is

We need to use the resolvent to solve this equation:

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