Particle A, which travels along the x-axis (the ground) is initially at rest at
ID: 2155145 • Letter: P
Question
Particle A, which travels along the x-axis (the ground) is initially at rest at the origin and has an acceleration of +8 m/s 2 . When A is at the origin, B is fired as a projectile 32 m directly above A at the angle shown. Determine a) the initial speed v0 of particle B required so that it strikes A, and b) the time required to do so. (Use g=10 m/s 2 .). It's a negative launch angle with a 3/4/5 right triangle, with the hypotenuse (5) being the path.
https://www.ualberta.ca/~kaminsky/Phys124S12/Phys 124 - Spring 2012 Assignment 2 Question 5.pdf (if it asks you to log in, it's username:robert password:hooke)
Help would be appreciated!
Explanation / Answer
Let it hit after time t
Hence both particles travel same distance in the positive x direction in this time
Hence Distance travelled by A in time t sec = (1/2)8*t2
Distance travelled by B horizontally in time t = v*(4/5) * t
Hence v*(4/5) * t = 4t2
Hence we have one equation as : v = 5t
Now taking downward motion into account; For b to strike A in has to move 32 m in t secs
Initial downward velocity = 3/5 v
Acceleration = g
Hence 32 = (3/5) vt + (1/2)gt2
Now using v = 5t here we get
32 = 3t2 + 5t2 = 8t2
Hence t2 = 4; t = 2 secs
Hencetime required for collision = 2 secs and initial velocity = 5*2 = 10 m/sec