PHYSM-我国在广东湛江以东海空域举行代号为“海上联合2019”的联合军事演习，在演习中一艘快艇以

我国在广东湛江以东海空域举行代号为“海上联合2019”的联合军事演习，在演习中一艘快艇以v1=40m/s的速度追击前面同一直线上正以速度v2=30m/s逃跑的敌舰。当两者相距L=3km时，发射一枚鱼雷，经过t1=50s，舰长通过望远镜看到了鱼雷击中敌舰发出的火花，敌舰被其击沉。（不考虑光传播的时间）求：（1）从发射鱼雷到击中敌舰，快艇以v1=40m/s的速度追了50s，此过程中我方快艇运动的距离s1为多少米？

Solution

a

Calculate the distance

s_1

that the fast boat travels while chasing the enemy ship. Use the equation

s = vt

since the speed

v_1

is constant

b

Substitute the given values into the equation:

s_1 = v_1 \times t_1

c

Compute the distance:

s_1 = 40 \, \text{m/s} \times 50 \, \text{s} = 2000 \, \text{m}

Answer

The fast boat travels a distance of

s_1 = 2000 \, \text{m}

while chasing the enemy ship.

Key Concept

Kinematics in one dimension: When an object moves with constant velocity, its displacement is given by the product of its velocity and the time of travel. Equation:

s = vt

Explanation

The fast boat moves with a constant velocity

v_1

, so the distance it covers in time

t_1

is simply the product of its speed and the time elapsed.

（2）鱼雷的速度v0为多少米每秒？

Solution

a

Calculate the relative speed between the torpedo and the enemy ship:

v_{rel} = v_1 - v_2

b

Substitute the given values:

v_{rel} = 40 \, \text{m/s} - 30 \, \text{m/s} = 10 \, \text{m/s}

c

Determine the distance covered by the torpedo:

d = v_{rel} \times t_1

d

Substitute the values to find the distance:

d = 10 \, \text{m/s} \times 50 \, \text{s} = 500 \, \text{m}

e

Add the distance covered by the fast boat to the initial separation to find the total distance covered by the torpedo:

d_{total} = L + s_1

f

Substitute the values for L and

s_1

:

d_{total} = 3000 \, \text{m} + 2000 \, \text{m} = 5000 \, \text{m}

g

Calculate the speed of the torpedo:

v_0 = \frac{d_{total}}{t_1}

h

Substitute the values to find

v_0

:

v_0 = \frac{5000 \, \text{m}}{50 \, \text{s}} = 100 \, \text{m/s}

Answer

鱼雷的速度

v_0

为 100 米每秒

Key Concept

Relative velocity and motion along a straight line: When two objects are moving along the same line, their relative velocity is the difference between their velocities. The distance covered by an object moving at a constant velocity is the product of its velocity and the time of travel.

Explanation

To find the torpedo's speed, we first determined the relative speed between the torpedo and the enemy ship, then calculated the total distance the torpedo traveled, and finally divided this distance by the time it took to hit the target.

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