While following the directions on a treasure map, a pirate walks 37.0 m north and then turns and walks 8.5 m east. What is the magnitude of his resultant displacement? (1 point)

Question

While following the directions on a treasure map, a pirate walks 37.0 m north and then turns and walks 8.5 m east. What is the magnitude of his resultant displacement? (1 point)

38 m
45.5 m
28.5 m

What is the direction (including angle) of the pirate's displacement in question #3? (1 point)
13º north of east
77º north of east
13º north
77º north

How fast must a truck travel to stay beneath an airplane that is moving 125 km/h at an angle of 35º to the ground? (1 point)
125 km/h
72 km/h
102 km/h
50 km/h

A baseball is thrown at an angle of 20º relative to the ground at a speed of 25.0 m/s. If the ball was caught 50.0 m from the thrower, how long was it in the air? (1 point)
2.1 seconds
0.5 seconds
10 seonds
5 seconds

How high did the baseball in question #5 travel before beginning it's descent? (1 point)
-4.5 m
3.5 m
50 m
10 m

Answer 1

some of the answers i gave are wrong!

Answer 2

To answer these questions, we can use basic trigonometry and vector addition. Let's go through each question step by step:

Question 1: The pirate first walks 37.0 m north and then 8.5 m east. To find the magnitude of the resultant displacement, we can use the Pythagorean theorem. The displacement in the north direction (vertical) is 37.0 m, and in the east direction (horizontal) is 8.5 m. Using the Pythagorean theorem (a^2 + b^2 = c^2), the magnitude of the resultant displacement is:

c = sqrt((37.0^2) + (8.5^2)) ≈ 38.10 m

So, the correct answer is 38 m.

Question 2: To find the direction of the pirate's displacement, we need to find the angle between the resultant displacement and the east direction. We can use trigonometry to find this angle. The angle (θ) can be found using the inverse tangent function:

θ = tan^(-1)(opposite/adjacent) = tan^(-1)(37.0/8.5) ≈ 77º

So, the correct answer is 77º north of east.

Question 3: The truck needs to travel at a certain speed to stay beneath an airplane that is moving at 125 km/h at an angle of 35º to the ground. We can use trigonometry again to solve this problem. The truck's speed needs to match the horizontal component of the airplane's velocity. The horizontal component can be found using the cosine function:

horizontal component = airplane speed * cos(angle)
horizontal component = 125 km/h * cos(35º) ≈ 102 km/h

So, the correct answer is 102 km/h.

Question 4: The baseball is thrown at an angle of 20º above the ground at a speed of 25.0 m/s. We can calculate the time of flight using the vertical motion of the projectile. The vertical displacement is 0 (since it starts and ends at the same level), and the initial vertical velocity is calculated as:

initial vertical velocity = initial speed * sin(angle)
initial vertical velocity = 25.0 m/s * sin(20º) ≈ 8.54 m/s

Using the equation of motion: displacement = (initial velocity * time) + (0.5 * acceleration * time^2), and substituting the variables, we can solve for time:

0 = (8.54 m/s * t) + (0.5 * (-9.8 m/s^2) * t^2)

Simplifying and solving this quadratic equation, we find two possible solutions for time: t = 0.494 seconds and t = 4.50 seconds. Since the ball is caught 50.0 m away from the thrower, it implies that the ball was in the air for t = 4.50 seconds.

So, the correct answer is 4.5 seconds.

Question 5: To find the height reached by the baseball, we can use the vertical motion of the projectile. The maximum height occurs when the vertical velocity becomes 0. We can calculate the time it takes to reach the maximum height using:

initial vertical velocity = 8.54 m/s (as calculated in question 4)
final vertical velocity = 0 m/s
acceleration = -9.8 m/s^2 (gravity pulling down)

Using the equation: final velocity = initial velocity + (acceleration * time), we can solve for time:

0 = 8.54 m/s + (-9.8 m/s^2) * t

Simplifying and solving for time, we find t ≈ 0.872 seconds.

To find the height reached, we can use the equation of motion: displacement = (initial velocity * time) + (0.5 * acceleration * time^2), and plug in the values:

displacement = (8.54 m/s * 0.872 s) + (0.5 * (-9.8 m/s^2) * (0.872 s)^2) ≈ 3.51 m

So, the correct answer is 3.5 m.

Answer 3

forgot to add my answers dang it. ok here:

1: i think its B.
2: i think its C????
3: not sure im stuck.
4: i believes its A.
5: ima say B and hope for the Best.