To develop this problem we will apply the concepts related to angular kinematic movement, related to linear kinematic movement. Linear velocity can be described in terms of angular velocity as shown below,
Here,
v = Lineal velocity
= Angular velocity
r = Radius
Our values are
Replacing to find the angular velocity we have,
Convert the units to RPM we have that
Therefore the angular speed of the wheels when the scooter is moving forward at 6.00 m/s is 955.41rpm
Answer:
θ₀ = 84.78° (OR) 5.22°
Explanation:
This situation can be treated as projectile motion. The parameters of this projectile motion are:
R = Range of Projectile = 150 m
V₀ = Launch Speed of Projectile = 90 m/s
g = 9.8 m/s²
θ₀ = Launch angle (OR) Angle of Elevation = ?
The formula for range of a projectile is given as:
R = V₀² Sin 2θ₀/g
Sin 2θ₀ = Rg/V₀²
Sin 2θ₀ = (150 m)(9.8 m/s²)/(90 m/s)²
2θ₀ = Sin⁻¹ (0.18)
θ₀ = 10.45°/2
<u>θ₀ = 5.22°</u>
Also, we know that for the same launch velocity the range will be same for complementary angles. Therefore, another possible value of angle is:
θ₀ = 90° - 5.22°
<u>θ₀ = 84.78°</u>
Let the key is free falling, therefore from equation of motion
.
Take initial velocity, u=0, so
.
As velocity moves with constant velocity of 3.5 m/s, therefore we can use formula
From above substituting t,
.
Now substituting all the given values and g = 9.8 m/s^2, we get
.
Thus, the distance the boat was from the point of impact when the key was released is 10.60 m.
Answer: The correct answer is B
Explanation: The string is pulling right and the string is unraveling causing it to accelerate left