A ball of mass 1 kg bounces vertically off the floor. Just before hitting the floor its velocity is 10 m/s downward. Just after
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Answer:
The depth to which the hydrometer sinks is approximately 24.07 cm
Explanation:
The given parameters are;
The diameter of the hydrometer tube, d = 2.3 cm
The mass of the content of the tube, m = 80 g
The density of the liquid in which the tube floats, ρ = 800 kg/m³
By Archimedes' principle, the up thrust (buoyancy) force acting on the hydrometer = The weight of the displaced liquid
When the hydrometer floats, the up-thrust is equal to the weight of the hydrometer which by Archimedes' principle, is equal to the weight of the volume of the liquid displaced by the hydrometer
Therefore;
The weight of the liquid displaced = The weight of the hydrometer, W = m·g
Where;
g = The acceleration due to gravity ≈ 9.81 m/s²
∴ W = 80 g × g
The volume of the liquid that has a mass of 80 g (0.08 kg), V = m/ρ
V = 0.08 kg/(800 kg/m³) = 0.0001 m³ = 0.0001 m³ × 1 × 10⁶ cm³/m³ = 100 cm³
The volume of the liquid displaced = 100 cm³ = The volume of the hydrometer submerged,
= A × h
Where;
A = The cross-sectional area of the tube = π·d²/4
h = The depth to which the hydrometer sinks
h = /A
∴ h = 100 cm³/( π × 2.3²/4 cm²) ≈ 24.07 cm
The depth to which the tube sinks, h ≈ 24.07 cm.
For the ball to go straight into the goal, the kicker needs to be no more than 6.54 meters away from the goal.
For the ball to arc into the goal, the kicker needs to be between 58.5 and 65.1 meters away from the goal.
<h3>Explanation</h3>How long does it take for the ball to reach the goal?
Let the distance between the kicker and the goal be meters.
Horizontal velocity of the ball will always be until it lands if there's no air resistance.
The ball will arrive at the goal in seconds after it leaves the kicker.
What will be the height of the ball when it reaches the goal?
Consider the equation
.
For this soccer ball:
,
,
since the player kicks the ball "from ground level."
when the ball reaches the goal.
.
Solve this quadratic equation for ,
.
meters when
meters.
or
meters when
meters.
In other words,
- For the ball to go straight into the goal, the kicker needs to be no more than 6.54 meters away from the goal.
- For the ball to arc into the goal, the kicker needs to be between 58.5 and 65.1 meters away from the goal.