Projectile motion (part 4) | One-dimensional motion | Physics | Khan Academy

TL;DR

The video explains how to calculate the time it takes for an object in projectile motion to hit the ground.

Transcript

We'll now use that equation we just derived to go back and solve-- or at least address-- that same problem we were doing before, so let's write that equation down again. Actually, let's write the problem down. Lets say I have the cliff again, and so my initial distance is 0, but it goes down 500 meters. I'm not going to redraw the cliff, because it... Read More

Key Insights

• ⌛ Projectile motion problems involve calculating various parameters such as time, distance, and velocity for objects moving in a curved path under the influence of gravity.
• 💩 The quadratic equation is often used to solve projectile motion problems that require finding the time to hit the ground or reach a certain height.
• 📉 Acceleration due to gravity is typically given a negative value to account for its downwards direction.
• 💱 The derived equation for change in distance combines initial velocity, time, and acceleration to determine the total change in vertical position.

Questions & Answers

Q: Why does acceleration due to gravity have a negative value?

Acceleration due to gravity is given a negative value because it always acts downwards, towards the center of the planet. This convention helps maintain the consistency of equations and calculations involving gravity.

Q: Can a negative time be meaningful in projectile motion problems?

No, a negative time does not make sense in projectile motion problems. It indicates a time before the object was launched or thrown. In the context of solving for time to hit the ground, only the positive root of the quadratic equation is considered as the valid time.

Q: How is the derived equation for change in distance derived?

The equation for change in distance, Δd = vi * t + (1/2) * a * t^2, is derived by integrating the equation for velocity, v = vi + a * t, with respect to time. The resulting equation relates the change in distance to the initial velocity, time, and acceleration.

Q: Why does it take longer for the object to hit the ground when thrown upwards compared to when it is simply dropped?

When thrown upwards, the object first slows down due to the deceleration caused by gravity, comes to a stop, and then accelerates downwards. As a result, it takes longer for the object to reach the ground because it has to cover a longer distance during the upward and downward motion.

Summary & Key Takeaways

• The video addresses solving a specific problem in projectile motion: determining the time it takes for an object to hit the ground.

• The problem involves a cliff, an initial distance of 0, a downward change in distance of 500 meters, an initial velocity of 30 m/s, and an acceleration of -10 m/s^2.

• The video derives an equation to calculate the change in distance based on the initial velocity, time, and acceleration, and uses the quadratic formula to solve for time.