Your book has applied the chain rule to produce:
dv/dt = dv/dx * dx/dt
Now, we can get dv/dx by:
1) Differentiate
x = vt, with respect to v.
dx/dv = t
Now, if we take the inverse of this, we can obtain dv/dx
dv/dx = 1/t
This is also proven by the fact that dv/dx is the change in velocity and if you multiply it by dv/dx, which is equivalent to dividing by the change in time, as we just proved, then you obtain acceleration.
Just because there is more mass in a certain substance doesn’t mean it’s density will change. In this case, water, will not change density simply because there is more of it. I.e the ocean. The bottom of the ocean may have more pressure to it because of the weight of the water above it but if you were to take a cup of it and take it to the surface it wouldn’t sink.
Answer:
0.83 m/s
Explanation:
FIrst of all, we have to find the time of flight, i.e. the time the baseball needs to reach the ground. This can be done by using the equation for the vertical motion:
where
h is the initial height
u = 0 is the initial vertical velocity
g = 9.8 m/s^2 is the acceleration of gravity
t is the time
Substituting h = 1.8 m and solving for t,
We know that the horizontal distance travelled by the ball is
d = 0.5 m
Therefore, we can find the horizontal velocity (which is constant during the whole motion):