A bush baby, an African primate, is capable of a remarkable...

Key Concepts

Acceleration due to Gravity

Acceleration due to gravity is the constant rate at which objects accelerate when in free-fall near the surface of the Earth, typically approximated as 9.8 m/s². It is essential for analyzing problems where an object transitions from a phase of powered acceleration to one where gravity is the only acting force, thereby influencing the object's trajectory and maximum height reached.

Projectile Motion

Projectile motion describes the motion of an object that is launched into the air and influenced only by gravity after launch. It is a two-phase process involving an initial phase with acceleration (or deceleration) due to applied forces and a subsequent free-flight phase where the motion is governed solely by gravitational acceleration. Understanding projectile motion helps in analyzing the transition from the powered phase to the free-fall phase.

Kinematic Equations

Kinematic equations are fundamental formulas in physics that describe the motion of objects under constant acceleration. They relate parameters such as displacement, initial and final velocities, acceleration, and time. These equations are especially useful in solving problems involving uniformly accelerated motion, such as determining the acceleration during a known distance when the final velocity is known or vice versa.

Uniform Acceleration

Uniform acceleration refers to motion where the rate of change of velocity is constant over time. In problems involving a constant pushing-off phase, the acceleration is assumed to be constant, allowing the use of kinematic equations to connect displacement and final velocity. This assumption simplifies the analysis by eliminating the need to consider varying forces during the motion.

Transcript

00:01 Alrighty.

00:03 Okay, so for this question, we have a jumping animal.

00:05 And the animal is going to start jumping.

00:07 So here's the ground.

00:09 We'll say that this is y equals zero.

00:12 We have an animal that's going to start jumping, accelerating upwards, for a height of, to a height of 0 .16 meters.

00:21 Okay.

00:23 And it's going to start jumping upwards and legs are extending, extending, extending for 1 .6 meters.

00:30 And then the legs are eventually going to leave the ground because we're jumping upwards.

00:36 And the animal is going to continue upwards for an additional 2 .3 meters.

00:46 2 .3 meters.

00:47 And we want to know what the acceleration of this period, so between this period of pushing off the ground, we want to know what the acceleration here is that will allow the animal to reach a total height of 2 .3 meters.

01:06 Ok.

01:07 So what we're given, we're given our displacements.

01:12 So we're jumping 0 .16 meters while we're constantly accelerating.

01:18 And then for this next region, this next region here, we're no longer touching the ground.

01:25 So the only acceleration we're subject to is the downward acceleration of gravity 9 .8 meters per second squared.

01:36 What else do we know? we know that once we reach the height, the apex of our jump up here, we know that our velocity is going to equal zero.

01:47 We're reaching our top.

01:48 And for an instant, it's going to be zero before we start falling back down.

01:53 And another thing that might be useful is the velocity at this point.

01:57 So when we draw our acceleration or a velocity curve, we know we're accelerating constantly.

02:04 Our velocity is increasing, increasing, increasing.

02:06 And then it's going to start deep.

02:09 Decreasing at a different rate, 9 .8 meters per second, until it's zero, and this is going to be the height of our jump here, zero velocity, and then we're going to start falling back to the ground.

02:25 So we're going to have a negative velocity, right? we're going to define the upward direction to be positive, the upward wide direction to be positive.

02:33 Okay, so we want to know essentially that this is a velocity versus time graph.

02:37 We want to know what this slope is here because we know that once we look, we leave the ground at this point right here in time at this point in time where it's going to the slope of acceleration is that it could be net or the velocity curve is going to be negative 9 .8 meters per cent square okay so where to start off so looking at our equations of motion the equation that stands out we we don't have anything in terms of time here we don't have anything in terms of time so we have we have displacements we have acceleration that we want to solve and we also have a final velocity here but we're going to split this problem up into two different regions we have region one region one and region two okay and we're going to do that because let me show you so region two region two when we when we look at the equation like i said we have everything in terms of displacements and acceleration so our equation our trusty equation of v1 squared equals v not squared plus two times acceleration times delta y in this case.

03:56 In region two, in region two, we know that our final velocity is going to be zero and our initial velocity we're going to have a certain speed.

04:10 We don't know what that is.

04:11 We don't know what that is.

04:12 But we do know we do know our acceleration is going to be negative 9 .8 meters per second squared and we do know our displacement.

04:19 That's going to be 2 .3 meters, 2 .3 meters.

04:24 Okay.

04:26 So now, now we can solve everything...