Calculating Image Size of Dropped Ball from a Concave Mirror

[patton_223]

Homework Statement

"a concave mirror is placed horizontally on the ground with a focal length of 1 meter, a boy sitting on a tree above the mirror drops a 7cm diameter styrofoam ball right over the mirror 3 meters high, determine when the image will be the same size of the ball"

Homework Equations

1/f= 1/Di + 1/Do

The Attempt at a Solution

i've found the distance of image when the ball is at 3M but i really don't know what to do from there. i honestly think there is no way of finding it, i think there's something missing (i may be wrong though lol)

 

[collinsmark]

Hello patton_223,

Welcome to Physics Forums!

i've found the distance of image when the ball is at 3M but i really don't know what to do from there. i honestly think there is no way of finding it, i think there's something missing (i may be wrong though lol)

Look up in your textbook/coursework about magnification (usually expressed with the variable M). You can express M as a ratio of image to object distances, and you can also express it in terms of a ratio of image size to object size. Combining equations and using substitution (including your 1/f = 1/D_o - 1/D_i formula), you can solve for the distance above the mirror.

By the way, "3 m high" means that the ball is 3 m above the mirror when time t = 0. Once you find the distance above the mirror where the image and object sizes are equal, use kinematics to find the time it takes for the ball to fall to that height.