The ball's horizontal and vertical velocities at time 
are
but the ball is thrown horizontally, so 
. Its horizontal and vertical positions at time are
The ball travels 22 m horizontally from where it was thrown, so
from which we find the time it takes for the ball to land on the ground is
When it lands, 
and
To solve this problem we will apply the concepts related to energy conservation. Here we will use the conservation between the potential gravitational energy and the kinetic energy to determine the velocity of this escape. The gravitational potential energy can be expressed as,
The kinetic energy can be written as,
Where,
Gravitational Universal Constant
Mass of Earth
Height
Radius of Earth
From the conservation of energy:
Rearranging to find the velocity,
Escape velocity at a certain height from the earth
If the height of the satellite from the earth is h, then the total distance would be the radius of the earth and the eight,
Replacing the values we have that
Therefore the escape velocity is 3.6km/s
Answer:
The right approach will be "47° north of east".
Explanation:
The given values are:
East of prison
= 1.70 km
Displacement vector
= 2.50 km
Now,
The direction will be:
⇒ 
⇒ 
⇒ 
i,e., 
(north of east)
Good work on solving part a).
b) may look complicated, but it's not too bad.
It says that the body is 25% efficient in converting fat to mechanical energy.
In other words, only 25% of the energy we get from our stored fat shows up
in the physical, mechanical moving around that we do. (The rest becomes
heat, which dissipates into the environment as we keep our bodies warm,
breathe hot air out,and perspire.)
You already know how much mechanical energy the climber needed to lift
himself to the top of the mountain... 2.4x10⁶ joules.
That's 25% of what he needs to convert in order to accomplish the climb.
He needs to pull 4 times as much energy out of fat.
-- Fat energy required = 4 x (2.4 x 10⁶) = 9.6 x 10⁶ joules.
-- Amount stored in 1kg of fat = 3.8 x 10⁷ joules
-- Portion of a kilogram he needs to use = (9.6 x 10⁶) / (3.8 x 10⁷)
Note:
That much of a kilogram weighs about 8.9 ounces ... which shows why it's so
hard to lose weight with physical exercise alone. It also helps you appreciate
that fat is much more efficient at storing energy than batteries are ... that one
kilogram of fat stores the amount of energy used by a 100-watt light bulb, to
burn for 105 hours (more than 4-1/2 days ! ! !)
Answer:
Vertical distance= 3.3803ft
Explanation:
First with the speed of the ball and the distance traveled horizontally we can determine the flight time to reach the plate:
Velocity= (90 mi/h) × (1 mile/5280ft) = 475200ft/h
Distance= Velocity × time⇒ time= 60.5ft / (475200ft/h) = 0.00012731h
time= 0.00012731h × (3600s/h)= 0.458316s
With this time we can determine the distance traveled vertically taking into account that its initial vertical velocity is zero and its acceleration is that of gravity, 9.81m/s²:
Vertical distance= (1/2) × 9.81 (m/s²) × (0.458316s)²=1.0303m
Vertical distance= 1.0303m × (1ft/0.3048m) = 3.3803ft
This is the vertical distance traveled by the ball from the time it is thrown by the pitcher until it reaches the plate, regardless of air resistance.
