Answer:
h = 0.46 m
Explanation:
According to the law of conservation of energy:
Potential Energy Lost by Roller Coaster = Kinetic Energy Gained by Roller Coaster
where,
h = height = ?
v = speed at bottom = 3 m/s
g = acceleration due to gravity = 9.81 m/s²
Therefore,
<u>h = 0.46 m</u>
Answer
a) Using dimensional analysis we cannot derive the relation, But we can check the correctness of the formula.
now, L H S
s = distance
dimension of distance = [M⁰L¹T⁰]
now, equation on the right hand side
R H S
u = speed
u = m/s
Dimension of speed = [M⁰L¹T⁻¹]
dimension of time
t = sec
Dimension of time = [M⁰L⁰T¹]
Dimension of 'ut' = [M⁰L¹T⁻¹][M⁰L⁰T¹]
= [M⁰L¹T⁰]
now, acceleration= a
a = m /s²
dimension of acceleration = [M⁰L¹T⁻²]
dimension of (at²) = [M⁰L¹T⁻²][M⁰L⁰T¹][M⁰L⁰T¹]
= [M⁰L¹T⁰]
hence, the dimension are balanced.
so, L H S = R H S
b) Moment of inertia of hollow sphere =
Moment of inertia of solid sphere =
we know,
Torque is the force that causes rotation
If the same amount of torque is applied to both spheres the sphere with bigger moment of inertia would have smaller angular velocity.
Thus the solid sphere would accelerate more.
Answer:
66.26 m/s
Explanation:
Horizontal velocity, Vx = 55.3 m/s
Vertical velocity, Vy = 36.5 m/s
The value of the resultant velocity is given by the vector sum of the two velocities which are acting at 90°.
V = 66.26 m/s
Thus, the velocity of the vehicle is 66.26 m/s along its descent path.