A stone is dropped into a river from a bridge 43.9 m above the water. Another stone is thrown v

A stone is dropped into a river from a bridge 43.9 m above...

A stone is dropped into a river from a bridge $43.9 \mathrm{~m}$ above the water. Another stone is thrown vertically down $1.00 \mathrm{~s}$ after the first is dropped. The stones strike the water at the same timc. (a) What is the initial speed of the scoond stonc? (b) Plot velocity versus time on a graph for each stone, taking zero time as the instant the first stone is released.

A stone is dropped into a river from a bridge $43.9 \mathrm{~m}$ above the water. Another stone is thrown vertically down $1.00 \mathrm{~s}$ after the first is dropped. The stones strike the water at the same timc. (a) What is the initial speed of the scoond stonc?
(b) Plot velocity versus time on a graph for each stone, taking zero time as the instant the first stone is released.

Key Concepts

Free Fall

This concept describes the motion of objects under the influence of gravity alone, with negligible air resistance. The acceleration is constant (denoted as g), allowing the use of standard kinematics equations. Free fall is key to understanding the displacement, velocity, and time relationships in any motion involving gravity.

Kinematic Equations

These equations provide the mathematical framework to analyze the motion of objects under constant acceleration. They relate displacement, initial velocity, time, and acceleration. In problems of free fall, equations such as s = ut + ½gt² and v = u + gt are fundamental for determining quantities like falling time and final velocity.

Time Delay in Projectile Motion

This concept addresses situations where two objects begin their motion at different times, but are analyzed within the same overall time frame. Understanding the impact of a delayed start is crucial for setting up the kinematic equations correctly and ensuring that the conditions for simultaneous events (like hitting the ground) are met.

Graphical Representation of Motion

Plotting velocity versus time graphs provides a visual illustration of an object’s motion under constant acceleration. These graphs help in understanding how initial velocities and time delays affect the overall motion, with the slope of the velocity-time graph representing acceleration. In such graphs, different starting times and initial velocities result in parallel lines that can intersect under specified conditions.

Transcript

00:01 In this problem of motion along a street line we have given that a stone is dropped into a river from a bridge which is 43 .9 meters above the water.

00:11 So, this is the water level.

00:13 Let's suppose this is the water level and this is the bridge which is 43 .9 meters above the water level.

00:24 And we have given that another stone is thrown vertically downwards one second after the first.

00:34 First is dropped.

00:36 That means first one is dropped and then after one second another stone is dropped.

00:44 Now we have asked that the stones strike the water at the same time.

00:53 That means first one is dropped.

00:56 That means it has been fallen under the free fall and then second has been thrown.

01:01 That means it has some initial velocity v and for the first stone, initial velocity say v i is equal to 0 and we have to find what is the initial speed of the second stone so first we have to find the time taken so this is given why h is equal to 43 .9 is equal to half and acceleration due to gravity this is 9 .8 and for time would be the same for both the stones because both are heating the water surface at the same time but initial time would be for the second stone would be t minus 1 so first we have to find the value of t so this is t is square now from here we say that t is equal to 2 multiplied with 43 .9 so this is 2 multiplied with 43 .9 divided with 9 .8 and now we have to take the under root and this value would be in 2nd so t is equal to here 2 .99 seconds so this is the time for this is the time for the first stone to be dropped.

02:15 And now for this second, this is we can say t1 that is time taken for the first stone to fall.

02:25 This is equal to 2 .99 second and t2 would be less than this is t1 by 1 second.

02:32 So this value would be 1 .99 seconds...

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