Here's a formula that's simple and useful, and if you're really in
high school physics, I'd be surprised if you haven't see it before.
This one is so simple and useful that I'd suggest memorizing it,
so it's always in your toolbox.
This formula tells how far an object travels in how much time,
when it's accelerating:
Distance = (1/2 acceleration) x (Time²).
D = 1/2 A T²
For your student who dropped an object out of the window,
Distance = 19.6 m
Acceleration = gravity = 9.8 m/s²
D = 1/2 G T²
19.6 = 4.9 T²
Divide each side by 4.9 : 4 = T²
Square root each side: 2 = T
When an object is dropped in Earth gravity,
it takes 2 seconds to fall the first 19.6 meters.
Answer:
The focal length of the appropriate corrective lens is 35.71 cm.
The power of the appropriate corrective lens is 0.028 D.
Explanation:
The expression for the lens formula is as follows;
Here, f is the focal length, u is the object distance and v is the image distance.
It is given in the problem that the given lens is corrective lens. Then, it will form an upright and virtual image at the near point of person's eye. The near point of a person's eye is 71.4 cm. To see objects clearly at a distance of 24.0 cm, the corrective lens is used.
Put v= -71.4 cm and u= 24.0 cm in the above expression.
f= 35.71 cm
Therefore, the focal length of the corrective lens is 35.71 cm.
The expression for the power of the lens is as follows;
Here, p is the power of the lens.
Put f= 35.71 cm.
p=0.028 D
Therefore, the power of the corrective lens is 0.028 D.
I'm going to assume that this gripping drama takes place on planet Earth, where the acceleration of gravity is 9.8 m/s². The solutions would be completely different if the same scenario were to play out in other places.
A ball is thrown upward with a speed of 40 m/s. Gravity decreases its upward speed (increases its downward speed) by 9.8 m/s every second.
So, the ball reaches its highest point after (40 m/s)/(9.8 m/s²) = <em>4.08 seconds</em>. At that point, it runs out of upward gas, and begins falling.
Just like so many other aspects of life, the downward fall is an exact "mirror image" of the upward trip. After another 4.08 seconds, the ball has returned to the height of the hand which flung it. In total, the ball is in the air for <em>8.16 seconds</em> up and down.
