# Two particles released from the same height and reached the base at the same time

**Problem**

Particles A and B are elevated 12 meters high from a given reference base. Particle A is projected down an incline of length 20 meters at the same time particle B is let to freely fall vertically. Find the velocity of projection of particle A if both particles strikes the base at the same time.

# Geometry-related Problems

**Example**

An isosceles triangle has an altitude equal to 12 inches and a perimeter equal to 36 inches. Find the length of the base and the length of the equal sides.

# 05 - Two runners moving in opposite directions in a circular track

**Problem**

Benjie and Jerwin is running in opposite directions in a 400-meter circular track and meet each other every 35 seconds. If Benjie can complete one track in 65 seconds. How long does it take for Jerwin to run 400 meters?

# 04 - Two runners moving in the same direction in an oval track

**Problem**

Runners A and B start together in a race around a 900-ft oval track. Runner A is making a speed of 27 ft/sec and runner B at 22.5 ft/sec. How long will it take runner A to be exactly one circumference ahead of runner B.

# 03 Maximum Revenue for Tour Bus of 80 Seats

**Problem**

A tour bus has 80 seats. Experience shows that when a tour costs P28,000, all seats on the bus will be sold. For each additional P1,000 charged, however, 2 fewer seats will be sold. Find the largest possible revenue.

A. P29,000

B. P28,500

C. P28,900

D. P28,700

# Reactions of Tripod Made from Wood Planks

**Situation**

In the figure shown, each plank carries a uniform load of 100 N/m throughout its length. The supports are on the same plane.

- Find the reaction at A.

A. 900 N

B. 800 N

C. 1400 N

D. 2400 N

- Find the reaction at B.

A. 900 N

B. 800 N

C. 1400 N

D. 2400 N

- Find the reaction at C.

A. 900 N

B. 800 N

C. 1400 N

D. 2400 N

# Support Reactions of a Trapezoidal Slab with Three Points of Support

**Situation**

A reinforced concrete slab in the shape of an isosceles trapezoid weighs 3600 N/m^{2}. It is supported on the three points as shown in the figure.

- Find the reaction at A.

A. 16,848 N

B. 6,716 N

C. 13,372 N

D. 2,010 N - Find the reaction at B.

A. 16,848 N

B. 6,716 N

C. 13,372 N

D. 2,010 N - Find the reaction at C.

A. 16,848 N

B. 6,716 N

C. 13,372 N

D. 2,010 N

# Trapezoidal gutter made from 24 m wide iron sheet

# 03 - In rowing a boat: find the rate of stream

**Problem**

A man can row 77 km and back in 14 hours. If he can row 6.5 km with the stream at the same time as 4.8 km against the stream, find the rate of the stream.