Pleas help exam tommarow Trigonometry word problems

[Aya]

Pleas help! exam tommarow! Trigonometry word problems

Hi, i really need help with this question,

on a wall, a spider is 100cm above a fly. the fly starts moving horizontally at the speed of 10cm/s. After 1s, the spider begins moving at twice the speed of the fly, in such a way as to intercept the fly by taking a straight line path. In what direction does the spider move, and how far has the fly moved when they meet?

How do I do this question? it just sayes the fly moved horizonally how do you know witch way it went, won't that determine where the spider went? and I oll have one measure ment 100cm? Can someone pleas help me throught the problem? I really don't know where to start

 

[HallsofIvy]

The fly is moving horizontally at 10 cm/s. In "t" seconds, it will have moved 10t cm from directly below the spider. If the spider at 20 cm/s, 1 second after the fly, t seconds after the fly started moving), it will have moved 20(t- 1) cm. (do you see why it is "t-1"?) If you draw the three lines connecting the spider's original position, the fly's original postion, and the point where they meet, you will have a right triangle with legs of length 100 cm and 10t cm, and hypotenuse of length 20(t-1) cm. Use the Pythagorean theorem to determine t and then use trig functions to determine the angles in the triangle.

 

[Architeuthis Dux]

.

Hi there,

I understand that you are feeling overwhelmed and unsure about how to approach this problem. Trigonometry word problems can be challenging, but with some guidance, you can definitely tackle it successfully.

Firstly, let's break down the problem into smaller parts. We have a fly and a spider, and they are both moving. We are given the initial position of the spider (100cm above the fly) and the speed of the fly (10cm/s). We are also told that the spider moves at twice the speed of the fly.

Now, let's think about the concept of intercepting. This means that the spider will move in such a way that it will meet the fly at some point. We don't know where exactly they will meet, but we do know that the spider will take a straight line path to get there.

Next, let's consider the direction of movement. Since the fly is moving horizontally, the spider must move in a direction that will intercept the fly. This means that the spider must move towards the fly, in the same direction that the fly is moving.

To solve this problem, we will need to use trigonometric functions, specifically the tangent function. The tangent function relates the opposite and adjacent sides of a right triangle. In this case, the horizontal distance that the fly moves will be the adjacent side, and the vertical distance that the spider moves will be the opposite side.

Now, we can set up a right triangle with the fly's starting position as the base, the spider's starting position as the height, and the distance they will meet as the hypotenuse. We can use the tangent function to find the angle at which the spider must move to intercept the fly. This angle will also give us the direction of the spider's movement.

To find the distance they will meet, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

I hope this explanation helps you understand the problem better and gives you a starting point for solving it. Remember to take your time, break the problem down into smaller parts, and use the appropriate trigonometric functions. Good luck on your exam tomorrow!