Maths4U Original · Short practice

A 7 kg particle starts from rest and slides 9 m down a line of greatest slope of a smooth fixed plane. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{3}{5},\quad\cos\alpha=\frac{4}{5}\). It meets no obstacle. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

Find the acceleration down the plane in \(\displaystyle \frac{m}{s^{2}}\).

Enter one exact number or fraction unless the question specifies rounding. Use the requested units and positive direction; enter the number without its unit. Angles here use degrees. Give full reasoning separately for written problems.

Maths4U Original · Short practice

A 8 kg particle starts from rest and slides 10 m down a line of greatest slope of a smooth fixed plane. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{5}{13},\quad\cos\alpha=\frac{12}{13}\). It meets no obstacle. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

Find the acceleration down the plane in \(\displaystyle \frac{m}{s^{2}}\).

Enter one exact number or fraction unless the question specifies rounding. Use the requested units and positive direction; enter the number without its unit. Angles here use degrees. Give full reasoning separately for written problems.

Maths4U Original · Short practice

A 8 kg particle starts from rest and slides 10 m down a line of greatest slope of a smooth fixed plane. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{5}{13},\quad\cos\alpha=\frac{12}{13}\). It meets no obstacle. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

Find its speed after the stated distance, in m/s to 3 significant figures.

Enter one exact number or fraction unless the question specifies rounding. Use the requested units and positive direction; enter the number without its unit. Angles here use degrees. Give full reasoning separately for written problems.

Maths4U Original · Short practice

A 2 kg particle starts from rest and slides 3 m down a line of greatest slope of a smooth fixed plane. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{8}{17},\quad\cos\alpha=\frac{15}{17}\). It meets no obstacle. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

Find its speed after the stated distance, in m/s to 3 significant figures.

Enter one exact number or fraction unless the question specifies rounding. Use the requested units and positive direction; enter the number without its unit. Angles here use degrees. Give full reasoning separately for written problems.

Maths4U Original · Short practice

A 2 kg particle starts from rest and slides 3 m down a line of greatest slope of a smooth fixed plane. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{8}{17},\quad\cos\alpha=\frac{15}{17}\). It meets no obstacle. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

Find the normal reaction in N.

Enter one exact number or fraction unless the question specifies rounding. Use the requested units and positive direction; enter the number without its unit. Angles here use degrees. Give full reasoning separately for written problems.

Maths4U Original · Short practice

A 3 kg particle starts from rest and slides 4 m down a line of greatest slope of a smooth fixed plane. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{3}{5},\quad\cos\alpha=\frac{4}{5}\). It meets no obstacle. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

Find the normal reaction in N.

Enter one exact number or fraction unless the question specifies rounding. Use the requested units and positive direction; enter the number without its unit. Angles here use degrees. Give full reasoning separately for written problems.

Maths4U Original · Short practice

A 3 kg particle starts from rest and slides 4 m down a line of greatest slope of a smooth fixed plane. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{3}{5},\quad\cos\alpha=\frac{4}{5}\). It meets no obstacle. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

Find the travel time in s, to 3 significant figures.

Enter one exact number or fraction unless the question specifies rounding. Use the requested units and positive direction; enter the number without its unit. Angles here use degrees. Give full reasoning separately for written problems.

Maths4U Original · Short practice

A 4 kg particle starts from rest and slides 5 m down a line of greatest slope of a smooth fixed plane. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{5}{13},\quad\cos\alpha=\frac{12}{13}\). It meets no obstacle. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

Find the travel time in s, to 3 significant figures.

Enter one exact number or fraction unless the question specifies rounding. Use the requested units and positive direction; enter the number without its unit. Angles here use degrees. Give full reasoning separately for written problems.