Online calculator: Vertical Collision Kinematics Calculator

The Vertical Collision Kinematics Calculator is designed to solve a specific problem related to the collision of two bodies. The problem involves two bodies being thrown vertically upward, one after the other, with the same speed 'v' after a time 't'. The calculator utilizes the laws of motion and gravitational force to determine the time and height at which the collision between the two bodies will occur.

To use the calculator, simply input the initial speed 'v' and the interval between throwings 't'. The calculator will then perform the necessary calculations to provide the time and height of collision.

The solution to this problem is based on the principles of kinematics and gravity. By analyzing the motion of the two bodies and considering the effects of gravity, the calculator determines the specific point at which their paths intersect. The solution is described below the calculator.

Kinematics. Throwing body up problem

Initial speed v (m/s)

Interval between throwings t, (s)

Calculation precision

Digits after the decimal point: 2

Time to collision t1, (s)

Collision height h, (m)

Solution

Distance traveled equation
$s(t)=v_0t+\frac{at^2}{2}$
For the first body
$y(t)=v(t+t_1)-\frac{g(t+t_1)^2}{2}$
For the second body
$y(t)=vt_1-\frac{gt_1^2}{2}$
Accordingly, when they meet, their coordinates will coincide, i.e.
$v(t+t_1)-\frac{g(t+t_1)^2}{2}=vt_1-\frac{gt_1^2}{2}$ ,
from which
$t_1=\frac{v}{g}-\frac{t}{2}$
After finding time, substitute it in any formula for the distance and find h
Gravitational acceleration is assumed to be equal 9.8 m/s²