Solving a Quadratic Equation for Projectile Motion

How to solve the equation “164 = 164 - 12t - 16t²”?

What are the possible solutions for t in the given equation?

Solution:

To solve the equation “164 = 164 - 12t - 16t²”, rearrange it into a quadratic equation and find the values of t that satisfy the equation. We can deduce two possible solutions for t: t = 0 or t = -3/4.

Explanation: The given equation is of a freely falling object, which is a subject matter of quadratic equations in Physics. Here, 164 represents the starting height in feet, -12t is the velocity at which the projectile is thrown downwards, and -16t² is the distance covered by the object under gravitational acceleration.

To solve the equation 164 = 164 - 12t - 16t², we need to rearrange it into a quadratic equation and find the values of t that satisfy the equation. Start by subtracting 164 from both sides to get 0 = -12t - 16t². Then, factor out a -4t from the right side to obtain 0 = -4t(3 + 4t). From this equation, we can deduce two possible solutions for t: t = 0 or t = -3/4.