Question Video: Studying the Motion of Bullets Horizontally Fired at Two Different Wooden Blocks | Nagwa Question Video: Studying the Motion of Bullets Horizontally Fired at Two Different Wooden Blocks | Nagwa

Question Video: Studying the Motion of Bullets Horizontally Fired at Two Different Wooden Blocks Mathematics • Second Year of Secondary School

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A bullet was fired horizontally at a wooden block. It entered the block at 80 m/s and penetrated 32 cm into the block before it stopped. Assuming that its acceleration 𝑎 was uniform, find 𝑎. If, under similar conditions, another bullet was fired at a wooden block that was 14 cm thick, determine the velocity at which the bullet exited the wooden block.

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Video Transcript

A bullet was fired horizontally at a wooden block. It entered the block at 80 meters per second and penetrated 32 centimeters into the block before it stopped. Assuming that its acceleration 𝑎 was uniform, find 𝑎. If under similar conditions, another bullet was fired at a wooden block that was 14 centimeters thick, determine the velocity at which the bullet exited the wooden block.

In our first scenario, we are told that a bullet is fired with velocity 80 meters per second. It penetrates 32 centimeters into the block. And as there are 100 centimeters in one meter, this is equal to 0.32 meters. To calculate the value of 𝑎, we will use the equations of uniform acceleration or SUVAT equations. We know that 𝑠, the displacement or distance, is equal to 0.32 meters, the initial velocity is 80 meters per second, the final velocity is zero meters per second, and we are trying to calculate the acceleration 𝑎. We will do this using the equation 𝑣 squared is equal to 𝑢 squared plus two 𝑎𝑠.

Substituting in our values gives us zero squared is equal to 80 squared plus two 𝑎 multiplied by 0.32. This simplifies to zero is equal to 6400 plus 0.64𝑎. We can then subtract 6400 from both sides and then divide by 0.64. This gives us a value of 𝑎 equal to negative 10000. The acceleration of the bullet is negative 10000 meters per second squared. As there are 1000 meters in a kilometer, this can also be written as negative 10 kilometers per second squared.

In our second scenario, the bullet travels straight through a wooden block of thickness 14 centimeters or 0.14 meters. Using the same values of 𝑢 and 𝑎, we can now calculate 𝑣, the velocity, at which the bullet exits the wooden block. We know that 𝑣 squared is equal to 𝑢 squared plus two 𝑎𝑠. Substituting in our values, we can calculate 𝑣 squared. This is equal to 3600. Square rooting both sides and knowing that 𝑣 must be positive, we get 𝑣 is equal to 60. The bullet exits the block at a velocity of 60 meters per second.

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