Question

A boy throws rocks with an initial velocity of 12m/s [down] from a 20 m bridge into a river. Consider the river to be at a height of 0 m. Draw a velocity-time and position-time graph. Use up as position and ignore air resistance.

Answer 1

Answer:

Please find attached the Velocity-Time graph, the Displacement-Time graph and the combined Velocity/Displacement-Time graph, created with Microsoft Excel

Explanation:

The given parameters are;

The initial velocity with which the boy throws the rock, u = 12 m/s

The direction in which he throws the rock = Down

The height from which the rock was thrown, h = 20 m

The height at which the river is located = 0 m

The kinematic equation of motion, of the rock can be given as follows;

h = u·t + 1/2·g·t²

Where;

t = The time of motion of the rock

g = The acceleration due to gravity = 9.8 m/s²

h = The height from which the rock is thrown = 20 m

Substituting the known values into given equation, we get;

20 = 12·t + 1/2·9.8·t² = 12·t + 4.9·t²

4.9·t² + 12·t - 20 = 0

t = (-12 ± √(12² - 4×4.9×(-20)))/(2 × 4.9) = (-12 ± √(242))/(9.8)

t ≈ -3.587 seconds or t ≈ 1.138 seconds

Attached please find the Velocity-Time graph, the Displacement-Time graph and the combined Velocity/Displacement-Time graph, created with Microsoft Excel.