A child throws a coin vertically downwards from a window of high building with an initial velocity of 15 m/s.Ignore the effect of air friction. Calculate vhow lonfg the coin falls
Wouldn't depend on the height?
To calculate how long the coin falls, we can use the equation of motion for vertical motion under constant acceleration. In this case, the acceleration is due to gravity and is approximately 9.8 m/s^2 downwards.
The equation to calculate the time taken for an object to fall vertically can be expressed as:
h = (1/2) * g * t^2
Where:
h is the vertical distance or height
g is the acceleration due to gravity
t is the time
In this case, the initial velocity is given as 15 m/s downwards, so it would be considered as the initial velocity in this equation.
Plugging in the values, we have:
0 = -15 * t + (1/2)(-9.8)(t^2)
Rearranging the equation, we get:
-4.9t^2 - 15t = 0
Factoring out t, we get:
t(-4.9t - 15) = 0
Now, we have two possibilities for t:
1) t = 0, which corresponds to the initial time when the coin is thrown
2) -4.9t - 15 = 0
To solve for t, we can set the equation -4.9t - 15 = 0 and solve for t.
-4.9t - 15 = 0
-4.9t = 15
t = 15 / -4.9
Evaluating this, we get:
t ≈ -3.061 sec
Since time cannot be negative, we discard the negative value.
Therefore, the time taken for the coin to fall is approximately 3.061 seconds.
To calculate how long the coin falls, we can use one of the equations of motion, specifically the equation for displacement in the vertical direction. The equation is:
s = ut + 0.5 * a * t^2
Where:
s - displacement (which is the distance the coin falls)
u - initial velocity (15 m/s in this case)
t - time taken
a - acceleration (which is the acceleration due to gravity, approximately 9.8 m/s^2)
Since the coin is thrown vertically downwards, we can assign the value of acceleration due to gravity as -9.8 m/s^2 (taking negative because it is directed downwards). Therefore, the equation becomes:
s = 15t - 0.5 * 9.8 * t^2
The coin falls until it reaches the ground, which means that the displacement (s) is equal to the height of the building. However, we need to know the height of the building to calculate exactly how long the coin falls.
Let's assume the height of the building is h meters. Setting s = h in the equation, we have:
h = 15t - 0.5 * 9.8 * t^2
This equation is a quadratic equation in terms of time (t), and we can solve it using various methods such as factoring, completing the square, or using the quadratic formula.
Once we solve the quadratic equation, it will give us two possible values of t (time). We discard the negative solution because time cannot be negative in this context. The positive solution will give us the time it takes for the coin to fall from the window to the ground, which is the answer to your question.