Answer:
No, the car will not make it to the top of the hill.
Explanation:
Let ΔX be how long the slope of the hill is, Δx be how far the car will travel along the slope of the hill, Ф be the angle the slope of the hill makes with the horizontal(bottom of the hill), ki be the kinetic energy of the car at the bottom of the hill and vi be the velocity of the car at the bottom of the hill and kf be the kinetic energy of the car when it stop moving at vf.
Since Ф is the angle between the horizontal and the slope, the relationship between the angle and the slope and the height of the hill is given by
sinФ = 12/ΔX
Which gives you the slope as
ΔX = 12/sinФ
Therefore for the car to reach the top of the hill it will have to travel ΔX.
Ignoring friction the total work done is given by
W = ΔK
W = (kf - ki)
Since the car will come to a stop, kf = 0 J
W = -ki
m×g×sinФ×Δx = 1/2×m×vi^2
(9.8)×sinФ×Δx = 1/2×(10)^2
sinФΔx = 5.1
Δx = 5.1/sinФ
ΔX>>Δx Ф ∈ (0° , 90°)
(Note that the maximum angle Ф is 90° because the slope of a hill can never be greater ≥ 90° because that would then mean the car cannot travel uphill.)
Since the car can never travel the distance of the slope, it can never make it to the top of the hill.
Answer: option D. 4
Reasoning:
Assuming that the time elapsed between any two consecutive dots is the same, and that the second dot marks second 1, the column with 3 dots marks second 2, and the dot right most marks second 3, the motorcycle has positive acceleration after 4 seconds.
That is because:
1) from the first dot to the second dot: the velocity the lenght of the arrow that models the velocity decrases, which means that the acceleration is negative.
2) In the nex group of dots the length of the arrow remains equal, which means that the velocity is constant and the acceleration is 0.
3) For the last dot, the length of the arrow is greater, which means that the velocity increases, and so the acceleration is positive.
The maximum height is:
hmax = v0² sin² α / 2 g<span>
The horizontal range is: x = v0² sin 2 α / g</span>
So we are given that:
x = 14.5 hmax
v0² sin 2 α / g
= 14.5 v0² sin² α / 2 g<span>
<span>7.25 sin² α = 2 sin α cos α
<span>7.25 sin α = 2 cos α
7.25 tan α = 2
<span>tan α = 0.27586
<span>α = tan^(-1) 0.27586
α = 15.42°<span>
<span>The angle of projection is 15.42</span></span><span>°</span></span></span></span></span></span>