Momentum and the archerfish. Archerfish are tropical fish that hunt by shooting drops of water from their mouths at insects above the water’s surface to knock them into the water, where the fish can eat them. A 65 g fish at rest just on the water’s surface can expel a 0.30 g drop of water in a short burst of 5.0 ms. High-speed measurements show that the water has a speed of 2.5 m/s just after the archerfish expels it. 77. What is the average force the fish exerts on the drop of water? A. 0.00015 N B. 0.00075 N C. 0.075 N D. 0.15 N
Momentum and the archerfish. Archerfish are tropical fish that hunt by shooting drops of water from their mouths at insects above the water’s surface to knock them into the water, where the fish can eat them. A 65 g fish at rest just on the water’s surface can expel a 0.30 g drop of water in a short burst of 5.0 ms. High-speed measurements show that the water has a speed of 2.5 m/s just after the archerfish expels it. 77. What is the average force the fish exerts on the drop of water? A. 0.00015 N B. 0.00075 N C. 0.075 N D. 0.15 N
Momentum and the archerfish. Archerfish are tropical fish that hunt by shooting drops of water from their mouths at insects above the water’s surface to knock them into the water, where the fish can eat them. A 65 g fish at rest just on the water’s surface can expel a 0.30 g drop of water in a short burst of 5.0 ms. High-speed measurements show that the water has a speed of 2.5 m/s just after the archerfish expels it.
77. What is the average force the fish exerts on the drop of water?
1.39 Given two vectors A = -2.00 +3.00 +4.00 and
B=3.00 +1.00 -3.00k. (a) find the magnitude of each vector;
(b) use unit vectors to write an expression for the vector difference
A - B; and (c) find the magnitude of the vector difference A - B. Is
this the same as the magnitude of B - Ä? Explain.
5. The radius of a circle is 5.5 cm.
(a) What is the circumference in meters?
(b) What is its area in square meters?
6. Using the generic triangle below, solve the following:
0 = 55 and c = 32 m, solve for a and b.
a = 250 m and b = 180 m, solve for the angle and c.
b=104 cm and c = 65 cm, solve for a and the angle
b
a
7. Consider the figure below representing the Temperature (T in degrees Celsius) as a function of time
t (in seconds)
4
12
20
(a) What is the area under the curve in the figure below?
(b) The area under the graph can be calculated using integrals or derivatives?
(c) During what interval is the derivative of temperature with respect to time equal to zero?
Part 3: Symbolic Algebra
Often problems in science and engineering are done with variables only. Don't let the different letters
confuse you. Manipulate them algebraically as though they were numbers.
1. Solve 3x-7= x + 3 for x
2x-1
2. Solve-
for x
2+2
In questions 3-11 solve for the required symbol/letter
3. v2 +2a(s-80), a =
=
4. B=
Ho I
2π r
5. K = kz²
6.xm=
MAL
,d=
d
7.T, 2
=
8.F=Gm
9. mgh=mv²
10.qV = mu²
80
12. Suppose that the height in meters of a thrown ball after t seconds is given by h =6+4t-t².
Complete the square to find the highest point and the time when this happens.
13. Solve by completing the square c₁t² + cat + 3 = 0.
14. Solve for the time t in the following expression = 0 + vot+at²
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