14. A bullet shot vertically upwards rises to a maximum height of 1000 m . Determine: (a) the initial velocity of the bullet. (b) the time of flight of the bullet.

Question

UpStudy AI · Accepted Answer

To determine the initial velocity of the bullet and the time of flight, we can use the equations of motion under gravity.

Given:
- Maximum height reached by the bullet = 1000 m

(a) To find the initial velocity of the bullet:
We know that the maximum height reached by a projectile under gravity is given by the equation:
$$ h = \frac{v_0^2}{2g} $$
where:
- $$ h $$ is the maximum height reached,
- $$ v_0 $$ is the initial velocity,
- $$ g $$ is the acceleration due to gravity (approximately 9.81 m/s^2).

Rearranging the equation to solve for $$ v_0 $$:
$$ v_0 = \sqrt{2gh} $$

(b) To find the time of flight of the bullet:
The time of flight of a projectile under gravity is given by the equation:
$$ t = \frac{2v_0}{g} $$

Now, we can calculate the initial velocity and the time of flight using the given maximum height.
Calculate the value by following steps:
- step0: Calculate:
  $$\sqrt{2\times 9.81\times 1000}$$
- step1: Multiply the terms:
  $$\sqrt{19620}$$
- step2: Write as a product:
  $$\sqrt{36\times 545}$$
- step3: Write in exponential form:
  $$\sqrt{6^{2}\times 545}$$
- step4: Use the properties of radicals:
  $$\sqrt{6^{2}}\times \sqrt{545}$$
- step5: Simplify the root:
  $$6\sqrt{545}$$
The initial velocity of the bullet is approximately 140.07 m/s.

Now, we can calculate the time of flight using the initial velocity.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{2\times 140.07}{9.81}$$
- step1: Multiply the numbers:
  $$\frac{280.14}{9.81}$$
- step2: Convert the expressions:
  $$\frac{\frac{14007}{50}}{\frac{981}{100}}$$
- step3: Multiply by the reciprocal:
  $$\frac{14007}{50}\times \frac{100}{981}$$
- step4: Reduce the numbers:
  $$4669\times \frac{2}{327}$$
- step5: Multiply:
  $$\frac{4669\times 2}{327}$$
- step6: Multiply:
  $$\frac{9338}{327}$$
The time of flight of the bullet is approximately 28.56 seconds.
(a) The initial velocity of the bullet is approximately 140.07 m/s. (b) The time of flight of the bullet is approximately 28.56 seconds.

A bullet shot vertically upwards rises
to a maximum height of 1000 m .
Determine:
(a) the initial velocity of the bullet.
(b) the time of flight of the bullet.

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Physics Questions