To solve this problem it is necessary to apply the kinematic equations of motion.
By definition we know that the position of a body is given by
Where
Initial position
Initial velocity
a = Acceleration
t= time
And the velocity can be expressed as,
Where,
For our case we have that there is neither initial position nor initial velocity, then
With our values we have , rearranging to find a,
Therefore the final velocity would be
Therefore the final velocity is 81.14m/s
Answer:
t = 1.58 s
Explanation:
given,
Speed of ranger, v = 56 km/h
v = 56 x 0.278 = 15.57 m/s
distance, d = 65 m
deceleration,a = 3 m/s²
reaction time = ?
using stopping distance formula
t is the reaction time
t = 1.58 s
hence, the reaction time of the ranger is equal to 1.58 s.
Answer:
D.
Explanation:
In order to know how long after Bill released his rock should Ted throw his if they want the stones to hit the water simultanously, we need to calculate the time needed to hit the water to both rocks independent each other, and just take the difference.
For the rock dropped by Bill, as the only influence on it is gravity (accelerating it downwards with an acceleration equal to g), and v₀ =0, we can use the following kinematic equation:
where y = height = 40 ft.
As all the parameters are given in SI units, it is advisable to convert this value to m, as follows:
Now, we can solve for t, as follows:
For the rock thrown down at 10 m/s, the kinematic equation we just have used becomes:
This leaves us a quadratic equation on t, as follows:
Taking the positive root, we have:
t = -1.02 s + 1.88 s = 0.86 s
So, in order to get that both rocks hit the water at the same time, Ted will need to wait the difference between both times:
Δt = 0.86 s - 1.58s = -0.72 s