a) 2.75 s
The vertical position of the ball at time t is given by the equation
where
h = 4 m is the initial height of the ball
u = 12 m/s is the initial velocity of the ball (upward)
g = 9.8 m/s^2 is the acceleration of gravity (downward)
We can find the time t at which the ball reaches the ground by substituting y=0 into the equation:
This is a second-order equation. By solving it for t, we find:
t = -0.30 s
t = 2.75 s
The first solution is negative, so we discard it; the second solution, t = 2.75 s, is the one we are looking for.
b) -15.0 m/s (downward)
The final velocity of the ball can be calculated by using the equation:
where
u = 12 m/s is the initial (upward) velocity
g = 9.8 m/s^2 is the acceleration of gravity (downward)
t is the time
By subsisuting t = 2.75 s, we find the velocity of the ball as it reaches the ground:
And the negative sign means the direction is downward.
Answer:
4.2 m/s
Explanation:
Momentum is conserved.
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
(35 g) (9 m/s) + (75 g) (-7 m/s) = (35 g) (-15 m/s) + (75 g) v
315 g m/s − 525 g m/s = -525 g m/s + (75 g) v
315 g m/s = (75 g) v
v = 4.2 m/s
gurlll this need way more points
1 horsepower is equal to 746 W, so the power of the engine is
The power is also defined as the energy E per unit of time t:
Where the energy corresponds to the work done by the engine, which is
. Re-arranging the formula, we can calculate the time t needed to do this amount of work:
Answer:
Explanation:
Acceleration of particle A is 7.3 times the acceleration of particle B.
Let the acceleration of particle B is a, then the acceleration of particle A is
7.3 a.
Let the period of particle A is T and the period of particle B is 2.5 T.
Let the radius of particle A is RA and the radius of particle B is RB.
Use the formula for the centripetal force
So, 
The ratio of radius of A to the radius of B is given by
RA : RB = 1.17
