1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
igomit [66]
3 years ago
9

In the latest Indian Jones film, Indy is supposed to throw a grenade from his car, which is going 81.0 km/h , to his enemy's car

, which is going 109 km/h . The enemy's car is 13.4 m in front of the Indy's when he lets go of the grenade.
A. If Indy throws the grenade so its initial velocity relative to him is at an angle of 45 above the horizontal, what should the magnitude of the initial velocity be? The cars are both traveling in the same direction on a level road. You can ignore air resistance.

B. Find the magnitude of the velocity relative to the earth.
Mathematics
1 answer:
Black_prince [1.1K]3 years ago
4 0

Answer:

  A.  18.21 m/s  or  65.6 km/h

  B.  135.5 km/h

Step-by-step explanation:

A. The vertical speed of the grenade is ...

  vv = v·sin(45°) = v/√2

The time in air is given by the equation for ballistic motion:

  h = -4.9t² +vv·t = 0

  t(vv -4.9t) = 0 . . . . . factor out t

  v/√2 = 4.9t

  v = t·4.9√2 . . . . . . solve for v

__

The horizontal distance the grenade travels in t seconds is ...

  d = vh·t = v·cos(45°)·t = vt/√2 = (t·4.9√2)(t/√2) = 4.9t² . . . . meters

1 m/s = 3.6 km/h, so the horizontal distance the target travels is ...

  x = (109 - 81.0)/3.6·t + 13.4 = 70t/9 +13.4 . . . . meters in t seconds

We want the target distance to be the same as the grenade's distance, so the time required to hit the target is ...

  d = x

  4.9t² = (70/9)t +13.4

  4.9(t² -(100/63)t) = 13.4

  4.9(t -50/63)² = 13.4 +4.9(50/63)² ≈ 16.486

  t = 50/63 + √(16.486/4.9) ≈ 2.62793 . . . seconds

This corresponds to a launch speed of ...

  v = (4.9√2)t ≈ 18.21 . . . . meters/second

__

B. As we said, 1 m/s = 3.6 km/h, so the launch speed is about 65.558 km/h at an angle of 45° relative to the direction of travel. The magnitude of the velocity relative to the earth (ve) will be this vector added to 81.0 km/h in the direction of travel. The (horizontal, vertical) components of that sum are ...

  (81.0, 0) + 65.558(cos(45°), sin(45°)) ≈ (127.357, 46.357) km/h

The magnitude is the Pythagorean sum:

  ve = √(127.357² +46.357²) ≈ 135.5 . . . . km/h

You might be interested in
Find the value of 7v-6 given that -8v-9=7 Simplify your answer as much as possible 7v-6=
evablogger [386]

Answer:

-20

Step-by-step explanation:

-8v-9=7

Add 9 to each side

-8v-9+9=7+9

-8v = 16

Divide by -8

-8v /-8 = 16/-8

v = -2

Now find

7v -6

7(-2) -6

-14 -6

-20

4 0
3 years ago
Read 2 more answers
Please help!!!!!!
Andre45 [30]

Since we know one root, which is -3, we can use synthetic division to find (x+3) would need to be multiplied by to get the original polynomial. Then, we factor the quadratic to find the other two factors, which are 1/2 and -2

3 0
3 years ago
Help with this !!! best answer excepted
Allushta [10]
Its 6 I think hope this helps


6 0
3 years ago
Read 2 more answers
A fish was swimming LaTeX: 2\frac{1}{2}2 1 2 feet below the water's surface at 1:00 p.M. Three hours later, the fish was at a de
marin [14]

Answer:

\frac{23}{4} feet

Step-by-step explanation:

The depth of the fish to the surface of water at 1:00 pm = 2 \frac{1}{2} feet

                                                                             =   \frac{5}{2} feet

The depth of the fish to its initial position at 4:00 pm = 3 \frac{1}{4} feet

                                                                              = \frac{13}{4} feet

The position of the fish with respect to the water's surface at 4:00 pm = the depth of the fish to the surface of water at 1:00 pm + the depth of the fish to its initial position at 4:00 pm

                                        =  \frac{5}{2} + \frac{13}{4}

                                        = \frac{10 + 13}{4}

                                         = \frac{23}{4}

The position of the fish with respect to the water's surface at 4:00 pm is \frac{23}{4} feet.

8 0
3 years ago
Given: AC = 4DC, BC = 4EC <br>Prove: A = D​
ella [17]
Two triangles that are proportional to each other and have the same angle are similar.
4 0
2 years ago
Other questions:
  • An equal number of students from two Algebra 1 classes at Bozeman School were randomly selected and asked how many hours per wee
    12·1 answer
  • 3. What is the area of the parallelogram below?
    7·1 answer
  • Evaluate the expression using the order of operations and rules for signed numbers. 6.8(6.7 – 7.2) – 2(4.6 + 1.2) =
    14·2 answers
  • There are two different loci that cause white coat color in horses. One locus is the albino locus found in all mammals. Albinism
    8·1 answer
  • For which value of x must the square root <br><br> 97x<br><br> be further simplified
    7·1 answer
  • Philip ran out of time while taking a multiple-choice test and plans to guess on the last 444 questions. Each question has 555 p
    8·1 answer
  • SOMEONE PLEASEEE HELPPP
    12·1 answer
  • Somebody help , i’ll thank you
    5·1 answer
  • Is the live tutoring over video, or do you type the question and send it to the tutor please explain?
    7·1 answer
  • A group of workers can plant 81 acres in 9 days. What is their rate in acres per day?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!