How Should the Child's Acceleration Be Calculated to Catch the Thrown Ball?

[Maximusw47]

Homework Statement

Starting from rest, a child throws a ball of mass m with an initial speed v , at an angle B with the horizontal direction. The child then chases after the ball, accelerating at a constant acceleration a . If the child wants to catch the ball at the same height as it was thrown, what must be the child's acceleration a ? Express your answer in terms of some or all of the variables v , m , B and g for the gravitational constant. Express the trigonometric functions in terms of the basic sin(B), cos(B) or tan(B).

Homework Equations

1-D Kinematics

The Attempt at a Solution

I'm using the point of release as the origin, positive-y is up and positive-x is the direction of the throw. I'm interested in the situation where at time t_f, x_child(t) = x_ball(t) and y_ball(t)=0. I start with the vertical.
t_f is the moment of the catch
v_yi is the initial vertical component of the ball's velocity; v_xi is the initial horizontal component of the ball's velocity

y(t)=v_yi*t-1/2*g*t^2
t_f=2*v_yi/g

For the horizontal component:
x_ball = v_xi*t
x_child = 1/2*a*t^2
At t_f:
v_xi*t_f=1/2*a*t_f^2
Substituting gives:
a=g*v_xi/v_yi

With vector decomposition I get an answer of:
a = g*v*cos(B)/sin(B)What am I doing wrong here?

 

[TSny]

Your work is very nicely written out .

Should the factor of v be in your final answer? Doesn't v cancel out?

 

[Maximusw47]

Your work is very nicely written out .

Should the factor of v be in your final answer? Doesn't v cancel out?

Thanks, that does indeed solve it. Perhaps one day I'll learn to do basic algebra.