Answer:
D
A machine can help decrease the input force and increase the output force.
D = distance between th two trains at the start of the motion = 100 miles
V = speed of the faster train towards slower train = 60 mph
v = speed of the slower train towards faster train = 40 mph
t = time taken by the two trains to collide = ?
time taken by the two trains to collide is given as
t = D/(V + v)
t = 100/(60 + 40) = 1 h
v' = speed of the bird = 90 mph
d = distance traveled by the bird
distance traveled by the bird is given as
d = v' t
d = 90 x 1
d = 90 miles
C because the air will push him closer to the space station
When hockey players push the puck along the ice it slides causing heat which melts the ice causing the friction against the ice to be less.
Answer:
The chance in distance is 25 knots
Explanation:
The distance between the two particles is given by:
(1)
Since A is traveling north and B is traveling east we can say that their displacement vector are perpendicular and therefore (1) transformed as:
(2)
Taking the differential with respect to time:
(3)
where
and
are the respective given velocities of the boats. To find
and
we make use of the given position for A,
, the Pythagoras theorem and the relation between distance and velocity for a movement with constant velocity.
![\displaystyle{y_A = v_A\cdot t\rightarrow t = \frac{y_A}{v_A}=\frac{30}{15}=2 h](https://tex.z-dn.net/?f=%5Cdisplaystyle%7By_A%20%3D%20v_A%5Ccdot%20t%5Crightarrow%20t%20%3D%20%5Cfrac%7By_A%7D%7Bv_A%7D%3D%5Cfrac%7B30%7D%7B15%7D%3D2%20h)
with this time, we know can now calculate the distance at which B is:
![\displaystyle{x_B = v_B\cdot t= 20 \cdot 2 = 40\ nmi](https://tex.z-dn.net/?f=%5Cdisplaystyle%7Bx_B%20%3D%20v_B%5Ccdot%20t%3D%2020%20%5Ccdot%202%20%3D%2040%5C%20nmi)
and applying Pythagoras:
![\displaystyle{s = \sqrt{x_B^2+y_A^2}=\sqrt{30^2 + 40^2}=\sqrt{2500}=50}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7Bs%20%3D%20%5Csqrt%7Bx_B%5E2%2By_A%5E2%7D%3D%5Csqrt%7B30%5E2%20%2B%2040%5E2%7D%3D%5Csqrt%7B2500%7D%3D50%7D)
Now substituting all the values in (3) and solving for
we get:
![\displaystyle{\frac{ds}{dt} = \frac{1}{2s}(2x_B\frac{dx_B}{dt}+2y_A\frac{dy_A}{dt})}\\\displaystyle{\frac{ds}{dt} = 25 \ knots}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Cfrac%7Bds%7D%7Bdt%7D%20%3D%20%5Cfrac%7B1%7D%7B2s%7D%282x_B%5Cfrac%7Bdx_B%7D%7Bdt%7D%2B2y_A%5Cfrac%7Bdy_A%7D%7Bdt%7D%29%7D%5C%5C%5Cdisplaystyle%7B%5Cfrac%7Bds%7D%7Bdt%7D%20%3D%2025%20%5C%20knots%7D)