A metal ball is thrown vertically upwards from the top of a tower with an initial velocity of 20 metres per seconds. If the ball took a total of 6 seconds to reach ground level, determine the height of the tower.
0 = h + Vi t - 4.9 t^2
or
0 = h + 20*6 - 4.9 * 36
To determine the height of the tower, we can use the equation of motion for an object under constant acceleration. In this case, the acceleration due to gravity is acting in the opposite direction to the initial velocity, so we will consider it as negative.
Let's break down the information given:
Initial velocity (u) = 20 m/s (upwards)
Time taken (t) = 6 seconds
Acceleration due to gravity (a) = -9.8 m/s² (negative since it acts in the opposite direction to the upwards direction of the ball)
We need to find the height (h) of the tower.
Using the equation of motion: h = ut + (1/2)at²
Substituting the given values:
h = (20 m/s)(6 s) + (1/2)(-9.8 m/s²)(6 s)²
Simplifying the equation:
h = 120 m + (1/2)(-9.8 m/s²)(36 s²)
h = 120 m - (4.9 m/s²)(36 s²)
h = 120 m - 176.4 m
h = -56.4 m
The negative sign indicates that the height is below the starting point. However, the height cannot be negative for a tower. Therefore, the answer is not plausible.
It's possible that there may be some missing information or an error in the given values.