Question

Будь ласка, допоможіть, дуже терміново!!! Стрілу було випущено з лука вертикально вгору з обриву заввишки 5 м. Стріла піднялася на 6 м над обривом і впала до його підніжжя. Визначте шлях і переміщення стріли за час польоту.

Answer 1

Problem Analysis

We are given that an arrow was shot vertically upwards from a cliff with a height of 5 meters. The arrow reached a maximum height of 6 meters above the cliff and then fell back down to the base of the cliff. We need to determine the distance traveled and the displacement of the arrow during its flight time.

Solution

To solve this problem, we need to consider the motion of the arrow in two phases: the upward motion and the downward motion.

# Upward Motion

During the upward motion, the arrow is subject to the force of gravity, which causes it to decelerate until it reaches its maximum height. At the maximum height, the arrow momentarily comes to a stop before starting its downward motion.

Let's denote the time taken for the upward motion as t1 and the distance traveled during this time as d1.

During the upward motion, the arrow experiences a constant acceleration due to gravity, which we can denote as g (approximately 9.8 m/s^2). The initial velocity of the arrow is 0 m/s at the start of the motion.

Using the kinematic equation d = v0 * t + (1/2) * a * t^2, where d is the distance traveled, v0 is the initial velocity, a is the acceleration, and t is the time, we can calculate the distance traveled during the upward motion:

d1 = 0 * t1 + (1/2) * g * t1^2

# Downward Motion

During the downward motion, the arrow is subject to the force of gravity, which causes it to accelerate downwards. The initial velocity of the arrow at the start of the downward motion is the same as the final velocity of the upward motion.

Let's denote the time taken for the downward motion as t2 and the distance traveled during this time as d2.

Using the same kinematic equation as before, we can calculate the distance traveled during the downward motion:

d2 = v1 * t2 + (1/2) * g * t2^2

where v1 is the final velocity of the upward motion, which is equal to the initial velocity of the downward motion.

# Total Flight Time

The total flight time of the arrow is the sum of the upward and downward motion times:

total flight time = t1 + t2

# Total Distance Traveled

The total distance traveled by the arrow is the sum of the distances traveled during the upward and downward motions:

total distance traveled = d1 + d2

# Displacement

The displacement of the arrow is the difference between the final and initial positions. In this case, the initial position is the base of the cliff and the final position is the maximum height reached by the arrow.

Let's denote the displacement as s.

s = maximum height - initial height

Now let's calculate the values using the given information.

Calculation

Given: - Height of the cliff (initial height) = 5 m