Answer:
6.78 m/s
Explanation:
Let the distance between the two friends is x .
Radius, r = 120 m
v = 7 m/s
Angular velocity, ω = v / r = 7 / 120 rad/s
Use the law of cosines for the triangle OAB
x^2 = 120^2 + 240^2 - 2 x 120 x 240 x Cosθ ...... (1)
differentiate with respect to t on both the sides
2 x dx/dt = - 57600 x (-Sinθ) dθ/dt
[tex]dx/dt=\frac{28800}{x}Sin\theta\times \omega[/tex] . ........ (2)
Put x = 240 m in equation (1), we get
240^2 = 120^2 + 24062 - 57600 Cosθ
Cosθ = 1/4
So, by the use of right angled triangle, Sinθ = √15/4
Put all the values in equation (2), we get
[tex]dx/dt=\frac{28800}{240}\times \frac{7}{120}\times \frac{\sqrt{15}}{4}[/tex]
[tex]dx/dt=\frac{7\sqrt{15}}{4}[/tex] m/s = 6.78 m/s
Answer:
speed = 6.78 m/s
Explanation:
Given Data
Radius=120 m
Constant Speed=7 m/s
Distance=240 m
To find
Speed=?
Solution
Angular velocity, ω = v / r = 7 / 120 rad/s
Use the law of cosines
x² = 120² + 240² - (2 x 120 x 240 x Cosθ ............eq(1)
differentiate with respect to t
2x (dx/dt) = - 57600 x (-Sinθ) dθ/dt..............eq(2)
Put x = 240 m in eq(1), we get
240² = 120² + 24062 - 57600 Cosθ
to find angle
Cosθ = 1/4
From the rule of right angled triangle
Sinθ = √15/4
Put all the values in equation (2), we get
2x (dx/dt) = - 57600 x (-Sinθ) dθ/dt
(dx/dt)=(7√15/4)
as we know that speed is first derivative with respect to time as acceleration is second derivative with respect to time
So
speed = 6.78 m/s
