Answer:
a) x(t) = 10t + (2/3)*t^3
b) x*(0.1875) = 10.18 m
Explanation:
Note: The position of the horse is x = 2m. There is a typing error in the question. Otherwise, The solution to cubic equation holds a negative value of time t.
Given:
- v(t) = 10 + 2*t^2 (radar gun)
- x*(t) = 10 + 5t^2 + 3t^3 (our coordinate)
Find:
-The position x of horse as a function of time t in radar system.
-The position of the horse at x = 2m in our coordinate system
Solution:
- The position of horse according to radar gun:
v(t) = dx / dt = 10 + 2*t^2
- Separate variables:
dx = (10 + 2*t^2).dt
- Integrate over interval x = 0 @ t= 0
x(t) = 10t + (2/3)*t^3
- time @ x = 2 :
2 = 10t + (2/3)*t^3
0 = 10t + (2/3)*t^3 + 2
- solve for t:
t = 0.1875 s
- Evaluate x* at t = 0.1875 s
x*(0.1875) = 10 + 5(0.1875)^2 + 3(0.1875)^3
x*(0.1875) = 10.18 m
Answer:
0
Explanation:
Given the following :
Height of wall = 19.2 m
Time taken to hit the ground = 5 seconds
Acceleration due to gravity (g) = 9.8m/s ( downward motion)
The initial velocity of the object refers to the Velocity of the object at time t = 0
Initial Velocity = g × time
Initial Velocity = 9.8 × 0 = 0
Answer:

Explanation:
We know the mass of the hole, so we define as,
kg
For which centripetal force is equal to gravitational force

Angular velocity is equal to v/r,

As r=1 and w=1, we clear to d,
m

Answer:
it must be helical motion in which the charge particle will move uniformly along z axis and simultaneously it will move in circular path in xy plane.
Explanation:
Magnetic field is along z axis while velocity is in x-z plane
so we will have

so here we can say

so we will have

so here the net force on the charge is perpendicular to its x directional velocity along - Y direction
So due to this component of motion it will move along a circle while other component of the motion will remain uniform always
So here it is combination of two parts
1) Uniform circular motion
2) Uniform motion
So we can say that it must be helical motion in which the charge particle will move uniformly along z axis and simultaneously it will move in circular path in xy plane.