a.how far does it travel horizontally while falling?
b. Find the horizontal and vertical components of its velocity when it strikes the earth.
Question A
Assuming that the friction of the air is not calculated in, we calculate as follows.
No matter what mass, all objects fall at the same rate and using the fomula
y = 1/2gt^2, we can calculate the time that it takes for the box to reach the ground.
y = 2000m
g = 9.8 m/s^2 (standard on earth)
2000 * 1/2 * 9.8 * t^2
t = 20.2s
So it takes 20.2 seconds for the box to reach the ground.
In these 20.2 seconds, it can travel horizontally according to the formula
x = vt
v = 150 m/s
t = 20.2
x = 150 * 20.2
x = 3030 m
It travels 3030m before reaching the ground.
Question B
Since its hard to factor in wind speed I’m guessing that for this answer, we can leave out the possibility of air friction.
If we do this, no other forces will stop the box from slowing down before hitting the ground. So the horizontal speed will remain constant at 150 m/s.
The object falls with an acceleration of 9.8m/s^2 (because this is what the g determines)
This means, each second, the speed of the object increases with 9.8 m/s
Since we start at v = 0 and we have 20.2 seconds for the fall
The speed just before it hits the ground would be
9.8 * 20.2 = 197.98 = 200m/s, rounded.
So the velocity components are
vy = 200 m/s
vx = 150 m/s
I’ve rounded the vy answer, so it might not be we 100% acurate, but this just looks nicer.
I hope this helps
Question A
Assuming that the friction of the air is not calculated in, we calculate as follows.
No matter what mass, all objects fall at the same rate and using the fomula
y = 1/2gt^2, we can calculate the time that it takes for the box to reach the ground.
y = 2000m
g = 9.8 m/s^2 (standard on earth)
2000 * 1/2 * 9.8 * t^2
t = 20.2s
So it takes 20.2 seconds for the box to reach the ground.
In these 20.2 seconds, it can travel horizontally according to the formula
x = vt
v = 150 m/s
t = 20.2
x = 150 * 20.2
x = 3030 m
It travels 3030m before reaching the ground.
Question B
Since its hard to factor in wind speed I’m guessing that for this answer, we can leave out the possibility of air friction.
If we do this, no other forces will stop the box from slowing down before hitting the ground. So the horizontal speed will remain constant at 150 m/s.
The object falls with an acceleration of 9.8m/s^2 (because this is what the g determines)
This means, each second, the speed of the object increases with 9.8 m/s
Since we start at v = 0 and we have 20.2 seconds for the fall
The speed just before it hits the ground would be
9.8 * 20.2 = 197.98 = 200m/s, rounded.
So the velocity components are
vy = 200 m/s
vx = 150 m/s
I’ve rounded the vy answer, so it might not be we 100% acurate, but this just looks nicer.
I hope this helps
References :
I’m a physics enthousiast