Question

Які значення кінетичної та потенціальної енергії стріли масою 50 г, випущеної з лука з швидкістю 30 м/с вертикально вгору, через 2 с після початку руху?

Answer 1

Через 2 с тело поднимется на высоту h=Vot-gt^2/2=30*2-5*4=40м
и будет иметь скорость v=Vo-gt=30-20=10м/с
тогда Ек= mv^2/2=0,05*100/2=2,5 Дж
Еп=mgh=0,05*10*40=20 Дж

Answer 2

Calculating Kinetic and Potential Energy of an Arrow

To calculate the kinetic and potential energy of an arrow with a mass of 50 g, launched vertically upward from a bow at a speed of 30 m/s after 2 seconds, we can use the following formulas:

1. Kinetic Energy (KE): - The kinetic energy of an object is given by the formula: \[ KE = \frac{1}{2}mv^2 \] where \( m \) is the mass of the object and \( v \) is its velocity.

2. Potential Energy (PE): - The potential energy of an object at a certain height is given by the formula: \[ PE = mgh \] where \( m \) is the mass of the object, \( g \) is the acceleration due to gravity, and \( h \) is the height.

Calculating Kinetic Energy

The kinetic energy of the arrow can be calculated using the formula: \[ KE = \frac{1}{2}mv^2 \] \[ KE = \frac{1}{2} \times 0.05 \times (30)^2 \] \[ KE = 22.5 \, \text{Joules} \]

The kinetic energy of the arrow is 22.5 Joules.

Calculating Potential Energy

To calculate the potential energy of the arrow, we need to determine the height it has reached after 2 seconds. This can be done using the equation of motion for an object under constant acceleration.

Given: - Initial velocity (\( u \)) = 30 m/s (upward) - Time (\( t \)) = 2 seconds - Acceleration due to gravity (\( g \)) = 9.81 m/s^2

Using the equation: \[ s = ut + \frac{1}{2}gt^2 \] \[ s = (30 \times 2) + \frac{1}{2} \times 9.81 \times (2)^2 \] \[ s = 60 + 19.62 \] \[ s = 79.62 \, \text{meters} \]

The arrow has reached a height of 79.62 meters.

Now, we can calculate the potential energy using the formula: \[ PE = mgh \] \[ PE = 0.05 \times 9.81 \times 79.62 \] \[ PE = 38.94 \, \text{Joules} \]

The potential energy of the arrow is 38.94 Joules.

Therefore, the kinetic energy of the arrow is 22.5 Joules and the potential energy is 38.94 Joules after 2 seconds of being launched vertically upward from the bow.