The rest energy of a particle is
where
is the rest mass of the particle and c is the speed of light.
The total energy of a relativistic particle is
where v is the speed of the particle.
We want the total energy of the particle to be twice its rest energy, so that
which means:
From which we find the ratio between the speed of the particle v and the speed of light c:
So, the particle should travel at 0.87c in order to have its total energy equal to twice its rest energy.
Answer:
32.3 m/s
Explanation:
The ball follows a projectile motion, where:
- The horizontal motion is a uniform motion at costant speed
- The vertical motion is a free fall motion (constant acceleration)
We start by analyzing the horizontal motion. The ball travels horizontally at constant speed of
and it covers a distance of
d = 165 m
So, the total time of flight of the ball is
In order to find the vertical velocity of the ball, we have now to analyze its vertical motion.
The vertical motion is a free-fall motion, so the ball is falling at constant acceleration; therefore we can use the following suvat equation:
where
is the vertical velocity at time t
is the initial vertical velocity
is the acceleration of gravity (taking downward as positive direction)
Substituting t = 3.3 s (the time of flight), we find the final vertical velocity of the ball:
Answer:12.206 cm,
Explanation:
Given
Insect walks 15 cm to the right
so its position vector is
Now it moves 10 cm up so its new position vector
Now it moves 8 cm left so its final position vector is
so its displacement is given by
For direction, let \theta is the angle made by its position vector with x axis
Answer:
Part a)
Part B)
Explanation:
Part A)
At the top of the hump the force on the rider is
1) Normal force
2) weight
so here we know that
Part B)
At the top of the loop we will have
in order to remain in contact the normal force must be just greater than zero
so we will have