An object is thrown downward with an initial
speed of 3 m/s from a height of 59 m above
the ground. At the same instant, a second
object is propelled vertically up from ground
level with a speed of 36 m/s .
At what height above the ground will the
two objects pass each other? The acceleration
of gravity is 9.8 m/s
2
.
Answer in units of m
speed of 3 m/s from a height of 59 m above
the ground. At the same instant, a second
object is propelled vertically up from ground
level with a speed of 36 m/s .
At what height above the ground will the
two objects pass each other? The acceleration
of gravity is 9.8 m/s
2
.
Answer in units of m
-
write the equations of motion for the two objects
y1(t)=59+3t-1/2gt^2
y2(t)=36t-1/2gt^2
set y1=y2:
59+3t - 1/2 gt^2 = 36 t -1/2gt^2
59=33t => t=59/33s
substitute this time into either y(t) equation to find the height of the objects at this time
y1(t)=59+3t-1/2gt^2
y2(t)=36t-1/2gt^2
set y1=y2:
59+3t - 1/2 gt^2 = 36 t -1/2gt^2
59=33t => t=59/33s
substitute this time into either y(t) equation to find the height of the objects at this time