Overview

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. Somebody throws a ball from the ground, and it just clears two walls, each five metres high: one wall is ten metres away, the other is thirty metres away. Where does the ball land? But wait, we don't know its speed, we don't know its angle. Can we still find it? Hold on to that thought. Today I will show you how to use this unit's problem bank, and then we will crack this puzzle with just one idea. And look, this is a JEE Advanced level problem, straight from this chapter. So, let's begin.

0:39What is in this chapter

So, first, what is this chapter? It is the problem bank for the whole kinematics unit: mixed solved problems, in three parts. Part A is at JEE Main level, okay? Part B is at JEE Advanced level, with longer problems. And Part C is concept checks. Short, but tricky, right? At the very end there is the unit test, and it has answers only. No worked solutions to lean on, so there you are on your own, just like in the exam hall. And one rule for the whole chapter: take g equal to ten. Here g is the acceleration due to gravity, and m s to the power minus two means metres per second squared. Ten keeps the numbers clean, doesn't it?

1:25Part A: a 40-minute test

Now, Part A, the JEE Main part. When should you attempt it? On the first day of the unit, just to see the questions? Not on day one! Only after Chapters one to seven, that is, once the whole unit is done. These problems mix every chapter, so you need all of them in your hand first. And attempt it as a test. Nineteen problems, forty minutes, a clock on the table. Exactly like the real paper, okay? So tell me. Nineteen problems in forty minutes: how much time do you get for each one? Forty divided by nineteen. The wavy equals sign means approximately: about two point one. So, a little over two minutes a problem. Keep an eye on the clock. Got it?

2:10Part B and Part C

Next, Part B, the JEE Advanced part. It has three big themes. First, variable acceleration: problems where the acceleration itself keeps changing. Second, projectiles that fly over obstacles, or are thrown from towers. Our two walls puzzle is exactly this type, right? And third, relative motion. Then Part C, the concept checks. They test the statements that come most often as true or false, or as assertion and reason. The slash means or, okay? Now, let me give you a taste. Can a body have zero velocity, but a non-zero acceleration? Yes, it can! Think of a ball thrown straight up. At the top, its velocity v is zero for an instant, but its acceleration a is still g. One line, and it checks whether your basics are really clear. Very important.

3:06Example 1: packet released from a rising balloon

Now, let's try one from Part A, and it is a medium one. Here is the question: a balloon is rising at ten metres per second; m s to the power minus one means metres per second. When it is forty metres above the ground, it releases a packet. When does the packet land? Pause the video, and try it first. Done? Okay, let's check. Many students say: the packet is released, so it simply drops from rest, right? No, no, careful! That is the trap. Just before the release, the packet was moving up with the balloon. So the packet starts with the balloon's velocity: u, its initial velocity, equals ten metres per second, upwards. It first rises a little, and only then comes down. Now take up as positive. The ground is forty metres below the release point, so the displacement is minus forty. Minus forty equals ten t, minus five t squared, where t is the time in seconds. Five t squared is half of g t squared, with g equal to ten. Clear? Bring everything to one side and divide by five: t squared minus two t minus eight equals zero. The double arrow means, so. It factorises as t minus four, into t plus two, equals zero. So t is four, or minus two. Which one do we keep? Four seconds, yes! Time cannot be negative. So the packet lands four seconds after it is released. See, one equation with the right sign covered the whole motion, up and down.

4:41Example 2: projectile that just clears two walls

Now, our puzzle from the start. This one is from Part B, and it is a hard one. Here it is: a projectile from the ground just clears two walls, each five metres high, at ten metres and thirty metres from the launch point. Find its range and its angle of projection. Pause the video, and try it. Done? Okay, let's check. Look at the figure. The ball is launched at speed u, at an angle theta; the orange u with an arrow on top is u vector. It rises to a height H and lands at a distance R, the range. The dashed line marks the top, exactly halfway, at R by two. The small arrows, v x, v y and u cos theta, and the speed u at landing, are about the velocity; we won't need them today. Now think: the path is symmetric about its top, and both walls have the same height. What does that tell you? Yes, exactly! The walls must sit symmetrically too, one on each side of the top, like mirror images, okay? So the first wall is ten metres after the launch point, and the second wall must be ten metres before the landing point. R equals ten plus thirty: forty metres! Notice, we never needed the speed. This is the topper's trick: symmetry first, algebra later. Now the angle. The path can be written as: y equals x tan theta, into one minus x by R, okay? Here x is the distance along the ground, and y is the height. With me? Put in the first wall: x equals ten, y equals five, and R equals forty. One minus ten by forty is three by four. So five equals ten tan theta, into three by four, okay? Now you finish it. Ten into three by four is what? And so, tan theta is? Ten into three by four is seven point five. So five equals seven point five tan theta, and tan theta equals two by three. Got it? Very good! So the angle of projection is tan inverse of two by three: the angle whose tan is two by three. Range forty metres, angle tan inverse two by three. And remember the start? We never knew the speed, and still we found where it lands. Clear?

7:04Quick revision: Parts A, B and C of the problem bank

So, quick revision. Part A is a forty minute test, after Chapters one to seven. Part B has the longer, JEE Advanced problems, and Part C checks your concepts. The unit test has answers only, and take g as ten throughout. Now set your clock, open Part A, and begin. You can do this, I promise. All the best!